Nonmonotone Adaptive Trust Region Algorithms with Indefinite Dogleg Path for Unconstrained Minimization

In this paper, we combine the nonmonotone and adaptive techniques with trust region method for unconstrained minimization problems. We set a new ratio of the actual descent and predicted descent. Then, instead of the monotone sequence, the nonmonotone sequence of function values are employed. With the adaptive technique, the radius of trust region △k can be adjusted automatically to improve the efficiency of trust region methods. By means of the Bunch-Parlett factorization, we construct a method with indefinite dogleg path for solving the trust region subproblem which can handle the indefinite approximate Hessian Bk. The convergence properties of the algorithm are established. Finally, detailed numerical results are reported to show that our algorithm is efficient.

A Backward Stable Hyperbolic QR Factorization Method for Solving Indefinite Least Squares Problem

We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward stable method proposed by Chandrasekaran, Gu and Sayed.

Differences in biological features of gastric dysplasia, indefinite dysplasia, reactive hyperplasia and discriminant analysis of these lesions

AIM: To investigate the differences in biological features of gastric dysplasia (Dys), indefinite dysplasia (IDys) and reactive hyperplasia (RH) by studying the biomarker alterations in cell proliferation, cell differentiation, cell cycle control and the expression of house-keeping genes, and further to search for markers which could be used in guiding the pathological diagnosis of three lesions. METHODS: Expressions of MUC5AC, MUC6, adenomatous polyposis coli (APC), p53, Ki-67, proliferation cell nuclear antigen (PCNA) and EGFR were studied by immunohistochemistry with a standard Envision technique in formalinfixed and paraffin-embedded specimens from 43 RH, 35 IDys, 35 Dys and 36 intestinal type gastric carcinomas (IGC). In addition, Bayes discriminant analysis was used to investigate the value of markers studied in differential diagnosis of RH, IDys, Dys and IGC. RESULTS: The MUC5AC and MUC6 antigen expressions in RH, IDys, Dys and IGC decreased gradually (MUC5AC:86.04%, 77.14%, 28.57%, 6.67%; MUC6: 65.15%, 54.29%, 20.00%, 25.00%, respectively). The expressions of the two markers had no significant difference between RH and IDys, but were all significantly higher than those ofthe other two lesions (MUC5AC: x2 = 27.607, 38.027 and 17.33, 26.092; MUC6: x2= 16.54, 12.665 and 9.282, 6.737, P＜0.01). There was no significant differencebetween RH and IDys, Dys and IGC in MUC6 expression. The APC gene expression in the four lesions had a similar decreasing tendency (RH 69.76%, IDys 68.57%, Dys39.39%, IGC 22.86%), and it was significantly higher in the first two lesions than in the last two (x2 = 7.011,16.995 and 14.737, 19.817, P＜0.05). The p53 expressionin RH, IDys, Dys and IGC was 6.98%, 20%, 57.14% and 50%, respectively. There was no significant differencebetween RH and IDys or Dys and IGC, but the p53 expression in RH and IDys was significantly lower than that in Dys and IGC (x2 = 7.011, 16.995 and 14.737, 19.817, P＜0.01).The Ki-67 label index was significantly different among four lesions (RH: 0.298±8.92%, IDys: 0.358±9.25%,Dys: 0.498±9.03%, IGC: 0.620±10.8%, P＜0.001). Positive immunostaining of PCNA was though observed in all specimens, significant differences were detected among four lesions (F= 95.318, P＜0.01). In addition, we used Bayes discriminant analysis to investigate molecular pathological classification of the lesions, and obtained the best result with the combination of MUC5AC, Ki-67 and PCNA. The overall rate of correct classification was67.4% (RH), 68.6% (IDys), 70.6% (Dys) and 84.8% (IGC), respectively.CONCLUSION: Dys has neoplastic biological characteristics, while RH and IDys display hyperplastic characteristics. MUC5AC and proliferation-related biomarkers (Ki-67, PCNA) are more specific in distinguishing Dys from RH and IDys.

Standing Waves for Quasilinear Schrödinger Equations with Indefinite Nonlinearity

In this article, we consider quasilinear Schrödinger equations of the form Such equations have been derived as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics. Unlike all known results in the literature, the nonlinearity is allowed to be indefinite. It is very interesting from physical and mathematical viewpoint. By mountain pass theorem and some special techniques, we prove the existence of solutions for the quasilinear Schrödinger equations with indefinite nonlinearity. This indefinite problem had never been considered so far. So our main results can be regarded as complementary work in the literature.

A Simple Method of Solving First-order Indefinite Equa tion

The current method of solving first order indefinite equatio n is changing the equation to first order indefinite equation gr oup to solve. But according this method, if variables are very many, it will be difficult to solve the equation using the current method. In this paper, it prov ides a simple method by discussing the structure of solution based on the theory of free abelian group. In addition, this method makes it easy to get the genera lized solution of the equation using the computer.

PRECONDITIONING MIXED ELEMENT METHOD FOR NONSELFADJOINT AND INDEFINITE SECOND ORDER ELLIPTIC PROBLEMS

In this paper, an equivalence between mixed element method and nonconforming element method for nonselfad joint and indefinite second order elliptic problems is established without using any bubble functions. It is proved that the H1-condition number of preconditioned operator Bh-1Ah is uniformly bounded and its Bh-singular values cluster in a positive finite interval, where Ah is the equivalent nonconforming element discretization of nonselfad joint and indefinite second order elliptic operator A, Bh is usual noncon forming element discretization of selfadjoint and positive definite second order elliptic operator B. Finally a simple V-cycle multigrid implementation of Bh-1 is given.

A uniqueness theorem for indefinite Sturm-Liouville operators

In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spectral sets {λn（q, ha,hk）}＋∞k=1 and {λ-n（q, hb,hk）}＋∞k=1 for distinct hk are sufficient to determine the potential q（x） on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.

Cyclic Group Action of Composite Order on Indefinite 4-manifolds

In this paper, we study the possibilities for several kinds of topological, locally linear cyclic group actions of non-prime order on some closed, simply connected 4-manifolds with indefinite intersection form. Especially, we discuss the existence of locally linear pseudofree C9 action on this kind of 4-manifolds.

Study on the Relation of Definite Integral and Indefinite Integral

Relation of definite integral and indefinite integral was discussed and an important result was gotten. If f(x) is bounded and has primary function, the formal definite integral x s f(t)dt is the indefinite integral of f(x), where x is a self-variable, s is a parameter,~f(x) is a function defined in(-∞, +∞), which comes from f(x) by restriction and extension. In other words, the indefinite integral is a special form of definite integral, its lower integral limit and upper integral limit are all indefinite.

Clinical significance and management of Barrett's esophagus with epithelial changes indefinite for dysplasia

Barrett's esophagus(BE) is defined as the extension of salmon-colored mucosa into the tubular esophagus ≥1 cm proximal to the gastroesophageal junction with biopsy confirmation of intestinal metaplasia. Patients with BE are at increased risk of esophageal adenocarcinoma(EAC), and undergo endoscopic surveillance biopsies to detect dysplasia or early EAC. Dysplasia in BE is classified as no dysplasia, indefinite for dysplasia(IND), low grade dysplasia(LGD) or high grade dysplasia(HGD). Biopsies are diagnosed as IND when the epithelial abnor-malities are not sufficient to diagnose dysplasia or the nature of the epithelial abnormalities is uncertain due to inflammation or technical issues. Specific diagnostic criteria for IND are not well established and its clinical significance and management has not been well studied. Previous studies have focused on HGD in BE and led to changes and improvement in the management of BE with HGD and early EAC. Only recently, IND and LGD in BE have become focus of intense study. This review summarizes the definition, neoplastic risk and clinical management of BE IND.

Characterizations of Null Holomorphic Sectional Curvature of GCR-Lightlike Submanifolds of Indefinite Nearly Khler Manifolds

We obtain the expressions for sectional curvature, holomorphic sectional curvature and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite nearly Kahler manifold and obtain characterization theorems for holo- morphic sectional and holomorphic bisectional curvature. We also establish a condi- tion for a GCR-lightlike submanifold of an indefinite complex space form to be a null holomorphically fiat.

Spectrum of a Class of Difference Operators with Indefinite Weights

In this study, we use analytical methods and Sylvester inertia theorem to research a class of second order difference operators with indefinite weights and coupled boundary conditions. The eigenvalue problem with sign-changing weight has lasted a long time. The number of eigenvalues and the number of sign changes of the corresponding eigenfunctions of discrete equations under different boundary conditions are mainly studied. For the discrete Sturm-Liouville problems, similar conclusions about the properties of eigenvalues and the number of sign changes of the corresponding eigenfunctions are obtained under different boundary conditions, such as periodic boundary conditions, antiperiodic boundary conditions and separated boundary conditions etc. The purpose of this paper is to extend the similar conclusion to the coupled boundary conditions, which is of great significance to the perfection of the theory of the discrete Sturm-Liouville problems. We came to the following conclusions: first, the eigenvalues of the problem are real and single, the number of the positive eigenvalues is equal to the number of positive elements in the weight function, and the number of negative eigenvalues is equal to the number of negative elements in the weight function. Second, under some conditions, we obtain the sign change of the eigenfunction corresponding to the j-th positive/negative eigenvalue.

A Characterization of Indefinite-unitary Invariant Linear Maps and Relative Results

Let ,4 and B be unital C＊-algebras, and let J∈A,L∈B be Hermitian invertible elements. For every T∈A and S∈B, define T^＋J=J^-1T＊J and ,S^＋L=^L-1,S＊L. Then in such a way we endow the C＊-algebras A and B with indefinite structures. We characterize firstly the Jordan （J, L）＋homomorphisms on C＊-algebras. As applications, we further classify the bounded linear maps Ф： A →B preserving （J, L）-unitary elements. When ,4 = B（H） and B=B（K）, where H and K are infinite dimensional and complete indefinite inner product spaces on real or complex fields, we prove that indefinite-unitary preserving bounded linear surjections are of the form T→UVTV^-1 （任意T∈B（H）） or T→UVT^＋V^-1（任意T∈B（H））, where U∈B（K） is indefinite unitary and, V ： H→ K is generalized indefinite unitary in the first form and generalized indefinite anti-unitary in the second one. Some results on indefinite orthogonality preserving additive maps are also given.

Solutions of Indefinite Equations

Indefinite equation is an unsolved problem in number theory. Through explo-ration, the author has been able to use a simple elementary algebraic method to solve the solutions of all three variable indefinite equations. In this paper, we will introduce and prove the solutions of Pythagorean equation, Fermat’s the-orem, Bill equation and so on.

Maximum Norm Estimates for Finite Volume Element Method for Non-selfadjoint and Indefinite Elliptic Problems

In this paper, we establish the maximum norm estimates of the solutions of the finite volume element method （FVE） based on the P1 conforming element for the non-selfadjoint and indefinite elliptic problems.

Uniform Convergence for Finite Volume Element Method for Non-selfadjoint and Indefinite Elliptic Problems

In this paper, we prove the existence, uniqueness and uniform convergence of the solution of finite volume element method based on the P1 conforming element for non-selfadjoint and indefinite elliptic problems under minimal elliptic regularity assumption.

ARBITRARILY SMALL NODAL SOLUTIONS FOR PARAMETRIC ROBIN(p,q)-EQUATIONS PLUS AN INDEFINITE POTENTIAL

We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavior near zero,we show that,for all λ>0 small,the problem has a nodal solution y_(λ)∈C^(1)(Ω)and we have y_(λ)→0 in C^(1)(Ω)asλ→0^(+).

DEFINITE PURSUITS IN AN INDEFINITE ERA

Today’s world has witnessed economic changes,political upheavals and restructuring of international relations.Europe since 2008 has experienced many problems including those from Greek debt crisis to euro zone crisis,from ownership of Crimea to Ukraine crisis,from long-lasting illegal migra-

HIERARCHICAL BASIS METHOD FOR COVOLUME METHOD FOR NONSYMMETRIC AND INDEFINITE ELLIPTIC PROBLEM

In this paper,hierarchical basis method for second order nonsymmetric andindefinite elliptic problem on a polygonal domain(possibly nonconvex)discreted by avertex-centered covolume method is constructed.

Capacitive Model and S-Parameters of Double-Pole Four-Throw Double-Gate RF CMOS Switch

In this paper, we have analyzed the Double-Pole Four-Throw Double-Gate Radio-Frequency Complementary Metal-Oxide-Semiconductor (DP4T DG RF CMOS) switch using S-parameters for 1 GHz to 60 GHz of frequency range. DP4T DG RF CMOS switch for operation at high frequency is also analyzed with its capacitive model. The re-sults for the development of this proposed switch include the basics of the circuit elements in terms of capacitance, re-sistance, impedance, admittance, series equivalent and parallel equivalent of this network at different frequencies which are present in this switch whatever they are ON or OFF.