Threefolds with vanishing Hodge cohomology

We consider algebraic manifolds of dimension 3 over with for all and 0$">. Let be a smooth completion of with , an effective divisor on with normal crossings. If the -dimension of is not zero, then is a fibre space over a smooth affine curve (i.e., we have a surjective morphism from to such that the general fibre is smooth and irreducible) such that every fibre satisfies the same vanishing condition. If an irreducible smooth fibre is not affine, then the Kodaira dimension of is and the -dimension of is 1. We also discuss sufficient conditions from the behavior of fibres or higher direct images to guarantee the global vanishing of Hodge cohomology and the affineness of .

     

Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable

We prove that finite quotients of the multiplicative group of a finite dimensional division algebra are solvable. Let be a finite dimensional division algebra having center , and let be a normal subgroup of finite index. Suppose is not solvable. Then we may assume that is a minimal nonsolvable group (MNS group for short), i.e. a nonsolvable group all of whose proper quotients are solvable. Our proof now has two main ingredients. One ingredient is to show that the commuting graph of a finite MNS group satisfies a certain property which we denote Property . This property includes the requirement that the diameter of the commuting graph should be , but is, in fact, stronger. Another ingredient is to show that if the commuting graph of has Property , then is open with respect to a nontrivial height one valuation of (assuming without loss of generality, as we may, that is finitely generated). After establishing the openness of (when is an MNS group) we apply the Nonexistence Theorem whose proof uses induction on the transcendence degree of over its prime subfield to eliminate as a possible quotient of , thereby obtaining a contradiction and proving our main result.

     

On sums of Darboux and nowhere constant continuous functions

We show that the property

(P)

for every Darboux function there exists a continuous nowhere constant function such that is Darboux

follows from the following two propositions:

(A)

for every subset of of cardinality there exists a uniformly continuous function such that ,

(B)

for an arbitrary function whose image contains a non-trivial interval there exists an of cardinality such that the restriction of to is uniformly continuous,

which hold in the iterated perfect set model.

     

Segmentation of synthetic aperture radar image using multiscale information measure-based spectral clustering

A multiscale information measure （MIM）, calculable from per-pixel wavelet coefficients, but relying on global statistics of synthetic aperture radar （SAR） image, is proposed. It fully exploits the variations in speckle pattern when the image resolution varies from course to fine, thus it can capture the intrinsic texture of the scene backscatter and the texture due to speckle simultaneously. Graph spectral segmen- tation methods based on MIM and the usual similarity measure are carried out on two real SAR images. Experimental results show that MIM can characterize texture information of SAR image more effectively than the commonly used similarity measure.     

Looking for Difference Sets in Groups with Dihedral Images

We prove four theorems about groups with a dihedral (or cyclic) image containing a difference set. For the first two, suppose G, a group of order 2p with p an odd prime, contains a nontrivial (v, k, ) difference set D with order n = k – prime to p and self-conjugate modulo p. If G has an image of order p, then 0 2a + 2 for a unique choice of = ±1, and for a = (k – )/2p. If G has an image of order 2p, then and ( – 1)/( – 1). There are further constraints on n, a and . We give examples in which these theorems imply no difference set can exist in a group of a specified order, including filling in some entries in Smith's extension to nonabelian groups of Lander's tables. A similar theorem covers the case when p|n. Finally, we show that if G contains a nontrivial (v, k, ) difference set D and has a dihedral image D _2m with either (n, m) = 1 or m = p ^t for p an odd prime dividing n, then one of the C ₂ intersection numbers of D is divisible by m. Again, this gives some non-existence results.     

Behaviors and mechanisms of copper adsorption on hydrolyzed polyacrylonitrile fibers

Polyacrylonitrile fiber (PANF) was hydrolyzed in a solution of sodium hydroxide and the hydrolyzed polyacrylonitrile fiber (HPANF) was used as an adsorbent to remove copper ions from aqueous solution. Scanning electron microscopy (SEM) showed that the hydrolysis process made the surface of HPANF rougher than that of PANF. Fourier transform infrared (FTIR) spectroscopy revealed that the HPANF contained conjugated imine (-Cz=Nz-) sequences. Batch adsorption results indicated that the HPANF was very effective in adsorbing copper, and the adsorption equilibrium could be reached within 10-20 min. Atomic force microscopy (AFM) showed that some aggregates formed on the surface of the HPANF after copper ion adsorption and the average surface roughness (R(a)) value of the HPANF changed from 0.363 to 3.763 nm due to copper adsorption. FTIR analysis indicated that copper adsorption caused a decrease of the light adsorption intensity of the imine (-Cz=Nz-) groups at 1573 and 1406 cm(-1) wavenumbers, and X-ray photoelectron spectroscopy (XPS) showed that the binding energy (BE) of some of the nitrogen atoms in the HPANF increased to a greater value due to copper adsorption. The FTIR and XPS results suggest that the adsorption of copper ions to the HPANF is attributed to the imine groups on the surface of the HPANF.     

How likely is Polya's drunkard to stay in x⩾ y⩾z?

In his celebrated paper, Polya has considered the random walk in the three-dimensional (cubic) lattice and showed that the probability of return to the origin is less than 1. Subsequent authors have shown that the probability is %34.053.... Here we consider the same random walk, with the restriction that the drunkard is only allowed to stay inxyz. It is shown that his probability of returning to the originand staying in the allowed region is %6.4844....     

Image sharing scheme based on combination theory

We present a simple algorithm for sharing and hiding secret image based on combination theory. The secret image is firstly encrypted by matrix multiplications and then shared into many shadow images by multiplying binary random sampling matrices. The sampling matrices randomly assign the pixel values to the shadow images which satisfy a specific combination rule as a constrain, so that the (t, n) threshold secret sharing scheme can be implemented. Numerical experiments have demonstrated the effectiveness of this image sharing algorithm.     

Structural evolution,growth mechanism and photoluminescence properties of CuWO4 nanocrystals

Copper tungstate (CuWO₄) crystals were synthesized by the sonochemistry (SC) method, and then, heat treated in a conventional furnace at different temperatures for 1 h. The structural evolution, growth mechanism and photoluminescence (PL) properties of these crystals were thoroughly investigated. X-ray diffraction patterns, micro-Raman spectra and Fourier transformed infrared spectra indicated that crystals heat treated and 100 °C and 200 °C have water molecules in their lattice (copper tungstate dihydrate (CuWO₄·2H₂O) with monoclinic structure), when the crystals are calcinated at 300 °C have the presence of two phase (CuWO₄·2H₂O and CuWO₄), while the others heat treated at 400 °C and 500 °C have a single CuWO₄ triclinic structure. Field emission scanning electron microscopy revealed a change in the morphological features of these crystals with the increase of the heat treatment temperature. Transmission electron microscopy (TEM), high resolution-TEM images and selected area electron diffraction were employed to examine the shape, size and structure of these crystals. Ultraviolet–Visible spectra evidenced a decrease of band gap values with the increase of the temperature, which were correlated with the reduction of intermediary energy levels within the band gap. The intense photoluminescence (PL) emission was detected for the sample heat treat at 300 °C for 1 h, which have a mixture of CuWO₄·2H₂O and CuWO₄ phases. Therefore, there is a synergic effect between the intermediary energy levels arising from these two phases during the electronic transitions responsible for PL emissions.     

基于图像块能量梯度的多聚焦图像融合

针对多聚焦图像,提出一种基于图像分块的融合方法。将源图像分为大小相同数量相等的子块,采用能量梯度算子作为对焦评价函数,计算各个图像子块能量梯度匹配度,设置匹配度阈值分离出源图像中的清晰区域。源图像中的清晰区域直接作为融合图像相应的区域,其它区域的处理中,构造与相应子块能量梯度大小相关的图像序列,以及像素点到各个子块中心距离相关的融合函数,然后用融合函数对图像序列融合。实验结果表明该方法有效性和合理性。