THE SHOCK WAVES FOR A MIXED-TYPE SYSTEM FROM CHEMOTAXIS

In this paper,we study the shock waves for a mixed-type system from chemotaxis.We are concerned with the jump conditions for the left state which is located in the elliptical region and the right state in the hyperbolic region.Under the generalized entropy conditions,we find that there are different shock wave structures for different parameters.To guarantee the uniqueness of the solutions,we obtain the admissible shock waves which satisfy the generalized entropy condition in both parameters.Finally,we construct the Riemann solutions in some solvable regions.

Differential analysis of lymph node metastasis in histological mixed-type early gastric carcinoma in the mucosa and submucosa

AIM To investigate the relationship between histological mixed-type of early gastric cancer(EGC) in the mucosa and submucosa and lymph node metastasis(LNM).METHODS This study included 298 patients who underwent gastrectomy for EGC between 2005 and 2012. Enrolled lesions were divided into groups of pure differentiated(pure D), pure undifferentiated(pure U), and mixed-type according to the proportion of the differentiated and undifferentiated components observed under a microscope. We reviewed the clinicopathological features, including age, sex, location, size, gross type, lymphovascular invasion, ulceration, and LNM, among the three groups. furthermore, we evaluated the predictors of LNM in the mucosa-confined EGC.RESULTS Of the 298 patients, 165(55.4%) had mucosa-confined EGC and 133(44.6%) had submucosa-invasive EGC. Only 13(7.9%) cases of mucosa-confined EGC and 30(22.6%) cases of submucosa-invasive EGC were observed to have LNM. The submucosal invasion(OR = 4.58, 95%CI: 1.23-16.97, P = 0.023), pure U type(OR = 4.97, 95%CI: 1.21-20.39, P = 0.026), and mixedtype(OR = 5.84, 95%CI: 1.05-32.61, P = 0.044) were independent risk factors for LNM in EGC. The rate of LNM in mucosa-confined EGC was higher in the mixedtype group(P = 0.012) and pure U group(P = 0.010) than in the pure D group, but no significant difference was found between the mixed-type group and pure U group(P = 0.739). Similarly, the rate of LNM in the submucosa-invasive EGC was higher in the mixedtype(P = 0.012) and pure U group(P = 0.009) than in the pure D group but was not significantly different between the mixed-type and pure U group(P = 0.375). Multivariate logistic analysis showed that only female sex(OR = 5.83, 95%CI: 1.64-20.70, P = 0.028) and presence of lymphovascular invasion(OR = 13.18, 95%CI: 1.39-125.30, P = 0.020) were independent risk factors for LNM in mucosa-confined EGC, while histological type was not an independent risk factor for LNM in mucosa-confined EGC(P = 0.106).CONCLUSION for mucosal EGC, histological mixed-type is not an independent risk factor for LNM and could be managed in the same way as the undifferentiated type.

Histological mixed-type as an independent prognostic factor in stageⅠgastric carcinoma

AIM: To evaluate the clinicopathological features of mixed-type gastric cancer and their influence on prognosis of mixed-type stageⅠgastric cancer.METHODS: We analyzed 446 patients who underwent curative gastrectomy for stageⅠgastric cancer between 1999 and 2009. The patients were divided into two groups: those with differentiated or undifferentiated cancer(non-mixed-type, n = 333) and those with a mixture of differentiated and undifferentiated cancers(mixed-type, n = 113).RESULTS: The overall prevalence of mixed-type gastric cancer was 25.3%(113/446). Compared with patients with non-mixed-type gastric cancer, those with mixedtype gastric cancer tended to be older at onset(P = 0.1252) and have a higher incidence of lymph node metastasis(P = 0.1476). They also had significantly larger tumors(P < 0.0001), more aggressive lymphatic invasion(P = 0.0011), and deeper tumor invasion(P < 0.0001). In addition, they exhibited significantly worse overall survival rates than did patients with non-mixedtype gastric cancer(P = 0.0026). Furthermore, mixedtype gastric cancer was independently associated with a worse outcome in multivariate analysis [P = 0.0300, hazard ratio = 11.4(1.265-102.7)].CONCLUSION: Histological mixed-type of gastric cancer contributes to malignant outcomes and highlight its usefulness as a prognostic indicator in stageⅠgastric cancer.

Using Link-Based Consensus Clustering for Mixed-Type Data Analysis

A mix between numerical and nominal data types commonly presents many modern-age data collections.Examples of these include banking data,sales history and healthcare records,where both continuous attributes like age and nominal ones like blood type are exploited to characterize account details,business transactions or individuals.However,only a few standard clustering techniques and consensus clusteringmethods are provided to examine such a data thus far.Given this insight,the paper introduces novel extensions of link-based cluster ensemble,LCEWCT and LCEWTQ that are accurate for analyzing mixed-type data.They promote diversity within an ensemble through different initializations of the k-prototypes algorithm as base clusterings and then refine the summarized data using a link-based approach.Based on the evaluationmetric of NMI(NormalizedMutual Information)that is averaged across different combinations of benchmark datasets and experimental settings,these new models reach the improved level of 0.34,while the best model found in the literature obtains only around the mark of 0.24.Besides,parameter analysis included herein helps to enhance their performance even further,given relations of clustering quality and algorithmic variables specific to the underlying link-based models.Moreover,another significant factor of ensemble size is examined in such a way to justify a tradeoff between complexity and accuracy.

A CLASS OF MIXED-TYPE FUNDAMENTAL PROBLEMS ON ELASTIC HALF-PLANE

The problems of equilibrium of an elastic half-plane with loads on some intervals of the boundary and zero displacements on its other parts are discussed. The solutions of such problems are expressed in terms of integrals by reducing them to Riemann boundary value problems. The analytic expressions of the solutions are obtained in cases of uniform loads. In particular, the solution is written in detail for the important case when uniform pressure is given on a single interval or two equal intervals.

A Note on Initial Value Problem for the Generalized Tricomi Equation in a Mixed-type Domain

In this paper, we study the well-posedness of initial value problem for n-dimensional gener-alized Tricomi equation in the mixed-type domain {（t,x）：t∈[1,＋∞）,x∈Rn} with the initial data given on the line t=1 in Hadamard＇s sense. By taking partial Fourier transformation, we obtain the explicit expression of the solution in terms of two integral operators and further establish the global estimate of such a solution for a class of initial data and source term. Finally, we establish the global solution in time direction for a semilinear problem used the estimate.

Development of Maritime Mix-Type Structures

Mixed-type structures combining the advantages of pile constructions(low material consumption and possibility to erect on weak soils)and gravity walls(high bearing capacity and stability,good reliability and durability)are considered and improved.The sphere of application,main peculiarities,and practical technological aspects of these structures’implementation are analyzed.

A DONNELL TYPE THEORY FOR FINITE DEFLECTION OF STIFFENED THIN CONICAL SHELLS COMPOSED OF COMPOSITE MATERIALS

A Donnell type theory is developed for finite deflection of closely stiffened truncated laminated composite conical shells under arbitrary loads by using the variational calculus and smeared-stiffener theory. The most general bending-stretching coupling and the effect of eccentricity of stiffeners are considered. The equilibrium equations, boundary conditions and the equation of compatibility are derived. The new equations of the mixed-type of stiffened laminated composite conical shells are obtained in terms of the transverse deflection and stress function. The simplified equations are also given for some commonly encountered cases.

Probability Models with Discrete and Continuous Parts

In mathematical statistics courses, students learn that the quadratic function is minimized when x is the mean of the random variable X, and that the graphs of this function for any two distributions of X are simply translates of each other. We focus on the problem of minimizing the function defined by in the context of mixtures of probability distributions of the discrete, absolutely continuous, and singular continuous types. This problem is important, for example, in Bayesian statistics, when one attempts to compute the decision function, which minimizes the expected risk with respect to an absolute error loss function. Although the literature considers this problem, it does so only under restrictive conditions on the distribution of the random variable X, by, for example, assuming that the corresponding cumulative distribution function is discrete or absolutely continuous. By using Riemann-Stieltjes integration, we prove a theorem, which solves this minimization problem under completely general conditions on the distribution of X. We also illustrate our result by presenting examples involving mixtures of distributions of the discrete and absolutely continuous types, and for the Cantor distribution, in which case the cumulative distribution function is singular continuous. Finally, we prove a theorem that evaluates the function y(x) when X has the Cantor distribution.

Regulation of Glucose Oxidase Activity through Interaction with Fullerene Derivatives

The 2-（hydroxymethyl）pyridine modified C60 （PY-C60） and methoxydiglycol modified C60 （MDG-C60） are synthesized using Bingel-Hirsch reaction and characterized by nuclear magnetic resonance （NMR） and mass spectra. PY-C60 and MDG-C60 can bind to glucose oxidase （GOx） and quench the fluorescence of tryptophan （Trp） residue in GOx through static mechanism. The conformation of GOx is disturbed after formation of complex with these fullerene derivatives. Kinetic analysis indicates that PY-C60 and MDG-C60 may affect the catalytic activity of GOx with a partial mixed-type inhibition mechanism. In the plasma glucose concentration range （3.6--5.2 mmol·L-1）, PY-C60 may significantly accelerate the catalytic velocity of GOx, however, MDG-C60 exerts almost no obvious change to the initial velocity of GOx, suggesting that elaborate design of molecular structure of fullerene derivative is very important for regulating the biological activity of fullerene-enzyme complex.

Lower-dimensional tori for generic Hamiltonian systems

For sufficient smooth nearly integrable Hamiltonian systems, an open dense set of perturbations has been constructed. And for a perturbation in this set the existence for families of lower-dimensional tori of hyperbolic, elliptic and mixed types has been proved.