Abstract:
In 1993 the Nunavut Land Claims Agreement (NLCA) was signed and this lead to the creation of Nunavut in 1999. Under the NLCA caribou and other wildlife in Nunavut are co-managed by government and Inuit. The Nunavut Wildlife Management Board (NWMB) is the main instrument of wildlife management, working with its government and Inuit co-management partners to manage caribou within the principles of conservation outlined in the NLCA, using both west ern scientific knowledge and traditional knowledge. When caribou herds cross provincial or territorial boundaries, management boards or management planning committees are established.

Abstract:
We discuss some of the limits of a methodology restricted to verificationism, the philosophy on which gene concatenation practices generally rely. As an alternative, we describe a software which identifies and focuses on impossible or refuted relationships, through a simple analysis of bootstrap bipartitions, followed by multivariate statistical analyses. We show how refuting phylogenetic relationships could in principle facilitate systematics. We also apply our method to the study of two complex phylogenies: the phylogeny of the archaea and the phylogeny of the core of genes shared by all life forms. While many groups are rejected, our results left open a possible proximity of N. equitans and the Methanopyrales, of the Archaea and the Cyanobacteria, and as well the possible grouping of the Methanobacteriales/Methanoccocales and Thermosplasmatales, of the Spirochaetes and the Actinobacteria and of the Proteobacteria and firmicutes.It is sometimes easier (and preferable) to decide which species do not group together than which ones do. When possible topologies are limited, identifying local relationships that are rejected may be a useful alternative to classical concatenation approaches aiming to find a globally resolved tree on the basis of weak phylogenetic markers.This article was reviewed by Mark Ragan, Eugene V Koonin and J Peter Gogarten.Reviewed by Mark Ragan, Eugene V Koonin and J Peter Gogarten. For the full reviews, please go to the Reviewers' comments section.Since the 1960's, molecular phylogeneticists have sought to reconstruct organismal relationships based on gene and protein trees [1]. Generally, successes in this enterprise have been evaluated as a function of the capacity to build unambiguous monophyletic groups, thus reducing the paraphyly of former classifications [2]. Despite such precise goals, tree reconstruction remains notoriously difficult, both for practical and conceptual reasons. Regarding some of the problems of classical phylogenetics,

Abstract:
Combining with the peculiarities of the claims of project equipments, firstly, this paper gives the concepts of the worthiness of project equipment, the project equipment contract depreciation and the project equipment contract agreement measuring. After analyzing the seed of affecting the project equipment worthiness, we offered the systemic analyzing method of finding affairs of the project equipments contract claims. Finally, the paper gives the model of ascertaining the amount of project equipments claims which based on the contract agreement measuring, and a case is successfully explained.

Abstract:
By using the explicit knowledge of the lowest energy single particle wave functions in the presence of an {\it arbitrary} magnetic field, we extend to the case of a torus Jain's idea of looking at the FQHE as a manifestation of an integer effect for {\it composite fermions}. We show that this can be realized thanks to a redefinition of the vacuum state that is explicitly collective in nature. We also discuss the relationship of this approach with the hierarchical scheme and with the characterization of the Hall states in terms of $W_{1+\infty}$ algebras and 2D conformal field theories.

Abstract:
In the present paper we discuss the approximation properties of Jain-Baskakov operators with parameter c. The present paper deals with the modified forms of the Baskakov basis functions. We establish some direct results, which include the asymptotic formula and error estimation in terms of the modulus of continuity and weighted approximation.

Abstract:
We obtain the clustering properties and part of the structure of zeroes of the Jain states at filling $\frac{k}{2k+1}$: they are a direct product of a Vandermonde determinant (which has to exist for any fermionic state) and a bosonic polynomial at filling $\frac{k}{k+1}$ which vanishes when $k+1$ particles cluster together. We show that all Jain states satisfy a "squeezing rule" (they are "squeezed polynomials") which severely reduces the dimension of the Hilbert space necessary to generate them. The squeezing rule also proves the clustering conditions that these states satisfy. We compute the topological entanglement spectrum of the Jain $\nu={2/5}$ state and compare it to both the Coulomb ground-state and the non-unitary Gaffnian state. All three states have very similar "low energy" structure. However, the Jain state entanglement "edge" state counting matches both the Coulomb counting as well as two decoupled U(1) free bosons, whereas the Gaffnian edge counting misses some of the "edge" states of the Coulomb spectrum. The spectral decomposition as well as the edge structure is evidence that the Jain state is universally equivalent to the ground state of the Coulomb Hamiltonian at $\nu={2/5}$. The evidence is much stronger than usual overlap studies which cannot meaningfully differentiate between the Jain and Gaffnian states. We compute the entanglement gap and present evidence that it remains constant in the thermodynamic limit. We also analyze the dependence of the entanglement gap and overlap as we drive the composite fermion system through a phase transition.

Abstract:
We analyze the modular properties of the effective CFT description for Jain plateaux corresponding to the fillings nu=m/(2pm+1). We construct its characters for the twisted and the untwisted sector and the diagonal partition function. We show that the degrees of freedom entering the partition function go to complete a Z_{m}-orbifold construction of the RCFT U(1)xSU(m)$ proposed for the Jain states. The resulting extended algebra of the chiral primary fields can be also viewed as a RCFT extension of the U(1)xW(m) minimal models. For m=2 we prove that our model, the TM, gives the RCFT closure of the extended minimal models U(1)xW(2).

Abstract:
We discuss d-wave topological (broken time reversal symmetry) pairing structures in unpolarized and polarized Jain states. We demonstrate pairing in the Jain spin singlet state by rewriting it in an explicit pairing form, in which we can recognize d-wave weak pairing of underlying quasiparticles - neutral fermions. We find and describe the root configuration of the Jain spin singlet state and its connection with neutral excitations of the Haldane-Rezayi state, and study the transition between these states via exact diagonalization. We find high overlaps with the Jain spin singlet state upon a departure from the hollow core model for which the Haldane-Rezayi state is the exact ground state. Due to a proven algebraic identity we were able to extend the analysis of topological d-wave pairing structures to polarized Jain states and integer quantum Hall states, and discuss its consequences.

Abstract:
We discuss stochastic calculus for large classes of Gaussian processes, based on rough path analysis. Our key condition is a covariance measure structure combined with a classical criterion due to Jain-Monrad [Ann. Probab. (1983)]. This condition is verified in many examples, even in absence of explicit expressions for the covariance or Volterra kernels. Of special interest are random Fourier series, with covariance given as Fourier series itself, and we formulate conditions directly in terms of the Fourier coefficients. We also establish convergence and rates of convergence in rough path metrics of approximations to such random Fourier series. An application to SPDE is given. Our criterion also leads to an embedding result for Cameron-Martin paths and complementary Young regularity (CYR) of the Cameron-Martin space and Gaussian sample paths. CYR is known to imply Malliavin regularity and also It\^o-like probabilistic estimates for stochastic integrals (resp. stochastic differential equations) despite their (rough) pathwise construction. At last, we give an application in the context of non-Markovian H\"ormander theory. The results include and extend those of [arXiv:1211.0046].

Abstract:
Generalization of Szász-Mirakyan operators has been considered by Jain, 1972. Using these generalized operators, we introduce new sequences of positive linear operators which are the integral modification of the Jain operators having weight functions of some Beta basis function. Approximation properties, the rate of convergence, weighted approximation theorem, and better approximation are investigated for these new operators. At the end, we generalize Jain-Beta operator with three parameters , , and and discuss Voronovskaja asymptotic formula. 1. Introduction For ,？？ , let then Equation (1) is a Poisson-type distribution which has been considered by Consul and Jain [1]. In 1970, Jain [2] introduced and studied the following class of positive linear operators: where and has been defined in (1). The parameter may depend on the natural number . It is easy to see that ; (3) reduces to the well-known Szász-Mirakyan operators [3]. Different generalization of Szász-Mirakyan operator and its approximation properties is studied in [4, 5]. Kantorovich-type extension of was given in [6]. Integral version of Jain operators using Beta basis function is introduced by Tarabie [7], which is as follows: In Gupta et al. [8] they considered integral modification of the Szász-Mirakyan operators by considering the weight function of Beta basis functions. Recently, Dubey and Jain [9] considered a parameter in the definition of [8]. Motivated by such types of operators we introduce new sequence of linear operators as follows: For and , where is defined in (1) and The operators defined by (5) are the integral modification of the Jain operators having weight function of some Beta basis function. As special case, the operators (5) reduced to the operators recently studied in [7]. Also, if and , then the operators (5) turn into the operators studied in [8]. In the present paper, we introduce the operators (5) and estimate moments for these operators. Also, we study local approximation theorem, rate of convergence, weighted approximation theorem, and better approximation for the operators . At the end, we propose Stancu-type generalization of (5) and discuss some local approximation properties and asymptotic formula for Stancu-type generalization of Jain-Beta operators. 2. Basic Results Lemma 1 (see [2]). For ,？？ , one has Lemma 2. The operators , defined by (5) satisfy the following relations: Proof. By simple computation, we get Lemma 3. For , , and with , one has (i) ,(ii) ？ . Lemma 4. For , , one has Proof. Since , , and , we have which is required. 3. Some Local Approximation