Abstract:
An association scheme is amorphous if it has as many fusion schemes as possible. Symmetric amorphous schemes were classified by A. V. Ivanov [A. V. Ivanov, Amorphous cellular rings II, in Investigations in algebraic theory of combinatorial objects, pages 39--49. VNIISI, Moscow, Institute for System Studies, 1985] and commutative amorphous schemes were classified by T. Ito, A. Munemasa and M. Yamada [T. Ito, A. Munemasa and M. Yamada, Amorphous association schemes over the Galois rings of characteristic 4, European J. Combin., 12(1991), 513--526]. A scheme is called skew-symmetric if the diagonal relation is the only symmetric relation. We prove the nonexistence of skew-symmetric amorphous schemes with at least 4 classes. We also prove that non-symmetric amorphous schemes are commutative.

Abstract:
Klebsiella pneumoniae is a facultative anaerobic gram-negative, non-motile, capsulated, gas-producing rod found widely in nature and often associated with urinary and respiratory infections in humans. Orbital cellulitis with abscess formation caused by K. pneumoniae is rare. Here, we present a case of K. pneumonia-inducing orbital cellulitis with abscess formation in a patient who had undergone an orbital wall fracture prosthesis with hydroxyapatite implantation due to orbital trauma 9 years ago. The patient was treated successfully with antibiotics and surgery.

Abstract:
n [D. de Caen, E.R. van Dam. Fissioned triangular schemes via the cross-ratio, {Europ. J. Combin.}, 22 (2001) 297-301], de Caen and van Dam constructed a fission scheme $\FT(q+1)$ of the triangular scheme on $\PG(1,q)$. This fission scheme comes from the naturally induced action of $\PGL(2,q)$ on the 2-element subsets of $\PG(1,q)$. The group $\PGL(2,q)$ is one of two infinite families of finite sharply 3-transitive groups. The other such family $\Mq(q)$ is a "twisted" version of $\PGL(2,q)$, where $q$ is an even power of an odd prime. The group $\PSL(2,q)$ is the intersection of $\PGL(2,q)$ and $\Mq(q)$. In this paper, we investigate the association schemes coming from the actions of $\PSL(2,q)$, $\Mq(q)$ and $\PML(2,q)$, respectively. Through the conic model introduced in [H.D.L. Hollmann, Q. Xiang. Association schemes from the actions of $\PGL(2, q) $ fixing a nonsingular conic, {J. Algebraic Combin.}, 24 (2006) 157-193], we introduce an embedding of $\PML(2,q)$ into $\PML(3,q)$. For each of the three groups mentioned above, this embedding produces two more isomorphic association schemes: one on hyperbolic lines and the other on hyperbolic points (via a null parity) in a 3-dimensional orthogonal geometry. This embedding enables us to treat these three isomorphic association schemes simultaneously.

Abstract:
In [H. Suzuki, Association schemes with multiple $Q$-polynomial structures, J. Algebraic Combin. 7 (1998) 181-196], Suzuki gave a classification of association schemes with multiple $Q$-polynomial structures, allowing for one exceptional case which has five classes. In this paper, we rule out the existence of this case. Hence Suzuki's theorem mirrors exactly the well-known counterpart for association schemes with multiple $P$-polynomial structures, a result due to Eiichi Bannai and Etsuko Bannai in 1980.

Abstract:
An association scheme is called skew-symmetric if it has no symmetric adjacency relations other than the diagonal one. In this paper, we study 4-class skew-symmetric association schemes. In J. Ma [On the nonexistence of skew-symmetric amorphous association schemes, submitted for publication], we discovered that their character tables fall into three types. We now determine their intersection matrices. We then determine the character tables and intersection numbers for 4-class skew-symmetric pseudocyclic association schemes, the only known examples of which are cyclotomic schemes. As a result, we answer a question raised by S. Y. Song [Commutative association schemes whose symmetrizations have two classes, J. Algebraic Combin. 5(1) 47-55, 1996]. We characterize and classify 4-class imprimitive skew-symmetric association schemes. We also prove that no 2-class Johnson scheme can admit a 4-class skew-symmetric fission scheme. Based on three types of character tables above, a short list of feasible parameters is generated.

Abstract:
It is known that a distance-regular graph with valency $k$ at least three admits at most two Q-polynomial structures. % In this note we show that all distance-regular graphs with diameter four and valency at least three admitting two $Q$-polynomial structures are either dual bipartite or almost dual imprimitive. By the work of Dickie \cite{Dickie} this implies that any distance-regular graph with diameter $d$ at least four and valency at least three admitting two $Q$-polynomial structures is, provided it is not a Hadamard graph, either the cube $H(d,2)$ with $d$ even, the half cube ${1}/{2} H(2d+1,2)$, the folded cube $\tilde{H}(2d+1,2)$, or the dual polar graph on $[^2A_{2d-1}(q)]$ with $q\ge 2$ a prime power.

Abstract:
Background MDM2 is a major negative regulator of p53, and a single nucleotide polymorphism (SNP) in the MDM2 promoter region SNP309 has been demonstrated to be associated with an increased MDM2 expression and a significantly earlier age of onset of several tumors, including gastric cancer. Several studies were published to evaluate the association between SNP309 and gastric cancer risk. However, the results remain conflicting rather than conclusive. Objective The aim of this study was to assess the association between the MDM2 SNP309 polymorphism and gastric risk. Methods We performed a meta-analysis to investigate this relationship. Odds ratios (ORs) and 95% confidence intervals (CIs) were used to assess the strength of the association. The pooled ORs were performed for codominant model, dominant model, and recessive model, respectively. Results Five published case-control studies, including 1,621 gastric cancer cases and 2,639 controls were identified. We found that the MDM2 SNP309 polymorphism was associated with a significantly increased risk of gastric cancer risk when all studies were pooled into the meta-analysis (GG versus TT, OR = 1.54; 95%CI = 1.04–2.29, and GG versus GT/TT, OR = 1.49, 95%CI = 1.30–1.72). Furthermore, Egger's test did not show any evidence of publication bias (P = 0.799 for GG versus TT). Conclusion Our results suggest that the MDM2 SNP309 polymorphism may be a low-penetrant risk factor for the development of gastric cancer.

Abstract:
In order to investigate the corrosion behavior of the sand screen material in stratum water, the corrosion of sand screen made of carbon/Alloy steels J55 is researched by changing the match of the Cl-, Ca2+ and the HCO3- in the stratum water saturated with CO2 to obtain the corrosion rate and slot width increment curve. Electron Microscopy is also used to acquire the corrosion morphology of the sample. The rule of the point corrosion and uniform corrosion is analyzed by combining the corrosion rate curve and corrosion morphology. The results show that the corrosion scale can be approximately divided into three layers. The outer layer is loose while the inner layer is compact. The corrosion rate and the slot width increment increase with the increasing of the ClG concentrations. However, the corrosion rate and slot width increment decrease with the increasing of the Ca2+ concentrations. The complexity of the HCO3- hydration results in the corrosion complexity. When the ClG concentrations are kept in a low level, serious pitting corrosion exists at most region of the sample surface. When the Cl- concentrations rise to a high level, the surface appears uniform corrosion. The existences of the Ca2+ help the sample resist from the further corrosion.

Abstract:
Two 3-dimensional global atmospheric transport models for persistent organic pollutants (POPs) have been employed to investigate the association between the large-scale atmospheric motions and poleward transports of persistent semi-volatile organic chemicals (SVOCs). We examine the modeled daily air concentration of α- and γ-hexachlorocyclohexane (HCH) over a period from 1997–1999 during which a number of episodic atmospheric transport events were detected in this modeling study. These events provide modeling evidence for improving the interpretation on the cold condensation effect and poleward atmospheric transport of SVOCs at the mid-troposphere. Two episodic transport events of γ-HCH (lindane) to the high Arctic (80–90° N), one from Asian and another from Eurasian sources, are reported in this paper. The both events suggest that the episodic atmospheric transports occurring at the mid-troposphere (e.g. from 3000–5500 m height) are driven by atmospheric horizontal and vertical motions. The association of the transport events with atmospheric circulation is briefly discussed. Strong southerly winds, forced by the evolution of two semi-permanent high pressure systems over mid-high latitudes in the Northern Hemisphere, play an important role in the long-range transport (LRT) of HCHs to the high latitudes from its sources. Being consistent with the cold condensation effect and poleward atmospheric transport in a mean meridional atmospheric circulation simulated by a 2-D atmospheric transport model, as reported by the first part of this study, this modeling study indicates that cold condensation is likely occurring more intensively at the mid-troposphere where rapid declining air temperature results in condensed phase of the chemical over and near its source regions and where stronger winds convey the chemical more rapidly to the polar region during the episodic poleward atmospheric transport events.