Periodic Solutions of Mixed Type p-Laplacian Equations with Deviating Arguments

Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,which are complement of previously known results.

PERIODIC BOUNDARY VALUE PROBLEMS FOR NONLINEAR IMPULSIVEINTEGRODIFFERENTIAL EQUATIONS OF MIXED TYPE IN BANACH SPACES

In this paper, the author obtains an existence theorem of minimal and maximal solutions for the periodic boundary value problems of nonlinear impulsive integrodifferential equations of mixed type in Banach space by means of the monotone iterative technique and cone theory based on a comparison result.

Mobola plum seed methanolic extracts exhibit mixed type inhibition of angiotensinⅠ-converting enzyme in vitro

Objective: To explore the possible inhibitory potentials and mechanism by Mobola plum(Parinari curatellifolia) seeds crude methanol(CE) and flavonoid-rich(FE) extracts on angiotensin-1-converting enzyme(ACE Ⅰ).Methods: The sensitivity and kinetic model of inhibition of CE and FE on ACE Ⅰ using N-[3-(2-furyl)-acryloyl]-Phe-Gly-Gly as enzyme substrate for ACE Ⅰ was evaluated by Michealis Menten approach. The inhibition mechanism was explored from Lineweaver–Burk model and IC_(50) was determined from Cheng–Prusoff empirical analysis.Results: The IC_(50) of CE and FE were 13.54 and 39.38 mg/m L, respectively. Both extracts exhibited mixed type inhibition with the inhibitory constant(K_i) of CE was between0.38 and 0.37 mg/m L while that of FE showed a two-fold increase(1.62 mg/mL and0.28 mg/mL). FE on ACE Ⅰ demonstrated positive cooperativity with a Hill's coefficient of1.89.Conclusions: The study reveals the superior ACE Ⅰ inhibitory potential of CE over FE and suggest that mixed inhibition pattern of the enzyme might be the underlying mechanism of antihypertensive activity.

A NONLINEAR LAVRENTIEV-BITSADZE MIXED TYPE EQUATION

In this paper the Tricomi problem for a nonlinear mixed type equation is studied. The coefficients of the mixed type equation are discontinuous on the line, where the equation changes its type. The existence of solution to this problem is proved. The method developed in this paper can be applied to study more difficult problems for nonlinear mixed type equations arising in gas dynamics.

UNIFORM BLOW-UP PROFILES FOR HEAT EQUATIONS WITH COUPLING NONLOCAL SOURCES OF ASYMMETRIC MIXED TYPE NONLINEARITIES

This article deals with a nonlocal heat system subject to null Dirichlet bound- ary conditions, where the coupling nonlocal sources consist of mixed type asymmetric non- linearities. We at first give the criterion for simultaneous blow-up of solutions, and then establish the uniform blow-up profiles of solutions near the blow-up time. It is observed that not only the simultaneous blow-up rates of the two components u and v are asymmet- ric, but also the blow-up rates of the same component u （or v） may be in different levels under different dominations.

PERIODIC BOUNDARY VALUE PROBLEMS FOR FIRST-ORDER INTEGRO-DIFFERENTIAL EQUATIONS OF MIXED TYPE

The existence of at feast one solution and the existence of extreme solutions of periodic boundary value problems for first-order integro-differential equations of mixed type are studied, in the presence of generalized upper and laver solutions. The discussion is based an new comparison theorems and coincidence degree and monotone iterative methods.

THE EXISTENCE OF PERIODIC SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS OF MIXED TYPE

The existence of periodic solutions for a class of impulsive differential equations of mixed type is studied by constructing periodic sequence solutions of difference equations.

Mixed type Ⅰ and Ⅱ choledochal cyst in an adult

BACKGROUND:Choledochal cysts are classified into five types based on the location of the cyst.Mixed types of choledochal cysts are extremely rare.Only five cases of mixed typeⅠandⅡcholedochal cysts have been reported, of which one was an adult case.We report a mixed typeⅠ andⅡcholedochal cyst in a 25-year-old man. METHODS:The unusual nature of the choledochal cyst, suspected on magnetic resonance cholangiopancreatography RCP to be typeⅠinitially,was confirmed by laparotomy to be a mixed typeⅠ+Ⅱcyst.Excision of the cyst and hepaticojejunostomy were performed. RESULT:The operation was uneventful,and the patient recovered well. CONCLUSIONS:Mixed type choledochal cysts are rare, and may be missed on imaging,unless careful evaluation is done.The operative method may not need to be modified significantly,as in the management of our case.

Strong Convergence Theorems for Mixed Type Asymptotically Nonexpansive Mappings

The purpose of this paper is to study a new two-step iterative scheme with mean errors of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings and prove strong convergence theorems for the new two-step iterative scheme in uniformly convex Banach spaces.

Recursive equations for compound distribution with the severity distribution of the mixed type

In this paper, recursive equations are obtained for compound distribution with the number of claims belonging to (a, b)-family and the severity distribution of the mixed type. Numerical methods to solve these equations are presented, and some numerical results are given.

COMPLETE EXTREMAL SURFACES OF MIXED TYPE IN 3-DIMENSIONAL MINKOWSKI SPACE

Many complete extremal surfaces of mixed type are constructed with explicit expressions. Itis proved that there exist complete extremal surfaces of mixed type which have a given numberof time-like spans and a given number of annular ends.

SOME NEW RESULTS FOR NONLINEAR BOUNDARY VALUE PROBLEMS OF MIXED TYPE INTEGRODIFFERENTIAL EQUATION

In this paper we give the existence and uniqueness of solutions for boundary value problems of the form u' = f(t, u,u', T1u,T2u), g(u(0),u(1)) = 0, h(w(0), u(1),u'(0), u'(1)) = 0 by means of the upper and lower solution method.

OBLIQUE DERIVATIVE BOUNDARY VALUE PROBLEMS OF MIXED TYPE EQUATION

In this article, the oblique derivative boundary value problems for the mixed type equation uxx＋sgnyuyy=aux＋buy＋cu＋d in another more general domain are discussed and by using the method of complex analysis, a series of solvability results is obtained, which generalizes some recent results.

Generalized Frankl-Rassias Mixed Type Equations in an Problem for a Class of Infinite Domain

In this paper, we study the boundary-value problem for mixed type equation with singular coefficient. We prove the unique solvability of the mentioned problem with the help of the extremum principle. The proof of the existence is based on the theory of singular integral equations, Wiener-Hopf equations and Fredholm integral equations.

Generalized Tricomi Problem for a Quasilinear Mixed Type Equation

In this paper,the Tricomi problem and the generalized Tricomi problem for a quasilinear mixed type equation are studied.The coefficients of the mixed type equation are discontinuous on the line,where the equation changes its type.The existence of solution to these problems is proved.The method developed in this paper can be used to study more difficult problems for nonlinear mixed type equations arising in gas dynamics.

A Class of Mixed Type Methods for Solving Stiff ODEs and Their Parallel Implementation

This paper presents a class of methods with high order, good stability, and complete parallelism.This paper first puts the conception of free parameter with which we can choose some parameters in these methods to make these methods more useable. For several cases, we give concrete formulas and obtain numerical results for several methods. Numerical experiments show that these methods are efficient in solving stiff ODEs with high dimension.

TRICOMI PROBLEM FOR A MIXED EQUATION OF SECOND ORDER WITH DISCONTINUOUS COEFFICIENTS

This paper is devoted to the Tricomi problem for a mixed type equation of second order. The coeffcients are assumed to be discontinuous on the line where the type is changed. The unique existence of the solution to the problem is proved if the domain is small enough. Correspondingly, some estimates on the solution is also established.

OSCILLATORY BEHAVIOR OF SOLUTIONS OF CERTAIN THIRD ORDER MIXED NEUTRAL DIFFERENCE EQUATIONS

The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form△（an△^2（xn＋bnxn-τ1＋cnxn＋τ2））＋qnx^βn＋1-σ1＋pnx^^βn＋1＋σ2=0,where （an）, （bn}, （cn}, （qn} and （pn} are positive real sequences, β is a ratio of odd positive integers, τ1, τ2, and σ2 are positive integers. We establish some sufficient conditions which ensure that all solutions are either oscillatory or converges to zero. Some examples are presented to illustrate the main results.

Two-Dimensional Riemann Problems:Transonic Shock Waves and Free Boundary Problems

We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.

Ruptured hepatoblastoma with massive internal bleeding in an adult

Hepatoblastoma is the most common primary hepatic tumor of children. However, only a very few cases have been reported in adults. Most studies support treatment with chemotherapy followed by surgical resection. We present the first reported case of adult hepatoblastoma in Taiwan. A 52-year-old female suffered from sudden onset of abdominal pain and general weakness for days.Internal bleeding with hemorrhagic shock was suspected and two massive lesions in both lobes of the liver with hemoperitoneum were noted from imaging studies.Surgical resection of the larger left lobe tumor and radio-frequency ablation of the right smaller one were performed. The histopathology diagnosis was of a hepatoblastoma.