Abstract:
We study the uniqueness of meromorphic functions concerning differential polynomials sharing fixed point and obtain some significant results , which improve the results due to Lin and Yi (2004). 1. Introduction and Main Results Let be a nonconstant meromorphic function in the whole complex plane . We will use the following standard notations of value distribution theory: , (see [1, 2]). We denote by any function satisfying possibly outside of a set with finite measure. Let be a finite complex number and a positive integer. We denote by the counting function for the zeros of in with multiplicity and by the corresponding one for which multiplicity is not counted. Let be the counting function for the zeros of in with multiplicity and the corresponding one for which multiplicity is not counted. Set Let be a nonconstant meromorphic function. We denote by the counting function for -points of both and about which has larger multiplicity than , where multiplicity is not counted. Similarly, we have notation . We say that and share CM (counting multiplicity) if and have same zeros with the same multiplicities. Similarly, we say that and share IM (ignoring multiplicity) if and have same zeros with ignoring multiplicities. In 2004, Lin and Yi [3] obtained the following results. Theorem A. Let and be two transcendental meromorphic functions, an integer. If and share CM, then either or where is a nonconstant meromorphic function. Theorem B. Let and be two transcendental meromorphic functions, an integer. If and share CM, then . In this paper, we study the uniqueness problems of entire or meromorphic functions concerning differential polynomials sharing fixed point, which improves Theorems A and B. 1.1. Main Results Theorem 1. Let and be two nonconstant meromorphic functions, a positive integer. If and share CM, and share IM, then either or where is a nonconstant meromorphic function. Theorem 2. Let and be two nonconstant meromorphic functions, a positive integer. If and share CM, and share IM, then . Theorem 3. Let and be two nonconstant entire functions, an integer. If and share CM, then . 2. Some Lemmas Lemma 4 (see [4]). Let , , and be nonconstant meromorphic functions such that . If , , and are linearly independent, then where and . Lemma 5 (see [1]). Let and be two nonconstant meromorphic functions. If , where , , and are non-zero constants, then Lemmas 4 and 5 play a very important role in proving our theorems. Lemma 6 (see [1]). Let be a nonconstant meromorphic function and let be a nonnegative integer, then The following lemmas play a cardinal role in proving

Abstract:
In this paper, we present a different and very simple technique to handle various uniqueness problems involving three small entire functions. It also gives a new additional insight into such problems.

Abstract:
What kind of lattice Hamiltonian manifestly has an ordered state with spontaneous orbital currents? We consider interacting spinless fermions on an array of square plaquettes, connected by weak hopping; the array geometry may be a 2 x 2L ladder, a 2 x 2 x 2L "tube", or a 2L x 2L square grid. At half filling, we derive an effective Hamiltonian in terms of pseudospins, of which one component represents orbital currents, and find the conditions sufficient for orbital current long-range order. We consider spinfull variants of the aforesaid spinless models and make contact with other spinfull models in the literature purported to possess spontaneous currents.

Abstract:
It is shown that the local density of states (LDOS), measured in an Scanning Tunneling Microscopy (STM) experiment, at a single tip position contains oscillations as a function of Energy, due to quasiparticle interference, which is related to the positions of nearby scatterers. We propose a method of STM data analysis based on this idea, which can be used to locate the scatterers. In the case of a superconductor, the method can potentially distinguish the nature of the scattering by a particular impurity.

Abstract:
We derive the shape of the high-energy features due to a weakly coupled boson in cuprate superconductors, as seen experimentally in Bi_2 Sr_2 Ca_1 Cu_2 O_8+x (BSCCO) by Lee et al. [Nature (London) 442, 546 (2006)]. A simplified model is used of d-wave Bogoliubov quasiparticles coupled to Einstein oscillators with a momentum-independent electron-boson coupling and an analytic fitting form is derived, which allows us (a) to extract the boson mode's frequency and (b) to estimate the electron-boson coupling strength. We further calculate the maximum possible superconducting gap due to an Einstein oscillator with the extracted electron-boson coupling strength, which is found to be less than 0.2 times of the observed gap indicating at the observed boson's non-dominant role in the superconductivity's mechanism. The extracted momentum-independent electron-boson coupling parameter (that we show a posteriori to indeed be in the weak-coupling regime) is then to be interpreted as an (band-structure detail dependent weighted) average over the Brillouin zone of the actual momentum-dependent electron-boson coupling in BSCCO.

Abstract:
We study the spin 1/2 quantum Heisenberg antiferromagnet on a Bethe lattice diluted to the percolation threshold. Dilution creates areas of even/odd sublattice imbalance resulting in "dangling spins" (L. Wang and A. W. Sandvik, Phys. Rev. Lett. 97, 117204 (2006); Phys. Rev. B 81, 054417 (2010)). These collectively act as "emergent" spin 1/2 degrees of freedom and are responsible for the creation of a set of low lying "quasidegenerate states". Using Density Matrix Renormalization Group (DMRG) calculations, we detect the presence and location of these emergent spins. We find an effective Hamiltonian of these emergent spins, with Heisenberg interactions that decay exponentially with the distance between them.

Abstract:
Assistive and intelligent learning system is one of the best alternatives to provide education to handicapped and disabled persons. This kind of learning system may work well because handicapped and disabled students will not be encountered with the limitations and problems of the conventional education systems. This assistive learning system is mainly a multi-agent system based scheme. Those agents are autonomous agents and they have the cognitive behaviour and adaptability. This scheme is based on the centralized as well as distributed multi-agent planning for agent communication, collaboration and negotiation.

Abstract:
This paper describes about the performance analysis of different data mining classifiers before and after feature selection on binomial data set. Three data mining classifiers Logistic Regression, SVM and Neural Network classifiers are considered in this paper for classification. The Congressional Voting Records data set is a binomial data set investigated in this study is taken from UCI machine learning repository. The classification performance of all classifiers is presented by using statistical performance measures like accuracy, specificity and sensitivity. Gain chart and R.O.C (Receiver Operating Characteristics) chart are also used to measure the performances of the classifiers. A comparative study is carried out among the data mining classifiers. Experimental result showed that without feature selection Logistic Regression and SVM classifiers provides 100% accuracy and neural network provides 98.13 % accuracy on test data set. With feature selection SVM classifier provides 100% accuracy. The performance of SVM classifier is found to be the best among all the classifiers with reduced number of features.

Abstract:
Based on Quasiparticle Interference(QPI) around a point impurity, we demonstrate an analysis scheme that extracts the lifetime of a quasiparticle by using the Local Density of States(LDOS) data around the impurity in a Scanning Tunneling Microscopy(STM) experiment. This data analysis scheme would augment the Fourier-Transform Scanning Tunneling Spectroscopic method which provides us with the quasiparticle dispersion. Thus, point impurities can be used as probes to extract quasiparticle lifetimes from STM experiments and this would complement other experimental methods such as Angle Resolved Photo-emission Spectrocopy(ARPES). We detail how the scheme would apply to conventional metals/Fermi Liquids and Superconductors.

We present a direct analytical algorithm for solving transportation problems with quadratic function cost coefficients. The algorithm uses the concept of absolute points developed by the authors in earlier works. The versatility of the proposed algorithm is evidenced by the fact that quadratic functions are often used as approximations for other functions, as in, for example, regression analysis. As compared with the earlier international methods for quadratic transportation problem (QTP) which are based on the Lagrangian relaxation approach, the proposed algorithm helps to understand the structure of the QTP better and can guide in managerial decisions. We present a numerical example to illustrate the application of the proposed method.