The tangential k-Cauchy-Fueter type operator and Penrose type integral formula on the generalized complex Heisenberg group

The tangential k-Cauchy-Fueter operator and k-CF functions are counterparts of the tangential Cauchy–Riemann operator and CR functions on the Heisenberg group in the theory of several complex variables,respectively.In this paper,we introduce a Lie group that the Heisenberg group can be imbedded into and call it generalized complex Heisenberg.We investigate quaternionic analysis on the generalized complex Heisenberg.We also give the Penrose integral formula for k-CF functions and construct the tangential k-Cauchy-Fueter complex.

Rational Invariants of the Generalized Classical Groups

In this paper,we give transcendence bases of the rational invariants fields of the generalized classical groups and their subgroups B,N and T,and we also compute the orders of them.Furthermore,we give explicit generators for the rational invariants fields of the Borel subgroup and the Neron-Severi subgroup of the general linear group.

The Invariant Rings of the Generalized Transvection Groups in the Modular Case

In this paper, first we investigate the invariant rings of the finite groups G ≤ GL（n, F;） generated by i-transvections and i-reflections with given invariant subspaces H over a finite field F;in the modular case. Then we are concerned with general groups G;（ω） and G;（ω）;named generalized transvection groups where ωis a k-th root of unity. By constructing quotient group and tensor, we calculate their invariant rings. In the end, we determine the properties of Cohen-Macaulay,Gorenstein, complete intersection, polynomial and Poincare series of these rings.

The Related Properties of Generalized Orthogonal Group in Specific Normed Linear Spaces

Firstly, in the general normed linear space, the concepts of generalized isosceles orthogonal group, generalized Birkhoff orthogonal group, generalized Roberts orthogonal group, strong Birkhoff orthogonal group and generalized orthogonal basis are introduced. Secondly, the conclusion that any two nonzero generalized orthogonal groups must be linearly independent group is proven. And the existence of nonzero generalized orthogonal group and its linear correlation are discussed preliminarily, as well as some related properties of nonempty generalized orthogonal group in specific normed linear space namely the lp space.

Generation of Spin 1 System

In this paper, we shall establish the connection between the group theory and quantum mechanics by showing how the group theory helps us to construct the spin operators. We look to the group generators SU (3). From these generators, new spin 1 operators will be constructed. These operators S-x, S-y and S-z satisfy all the properties of Pauli spin operators S-x, S-y and S-z. We shall discuss the notion of spin squeezing and correlations for pure spin 1 system using our spin operators S-x, S-y and S-z.

Generalization of Spin Operators

The study shall look to the group of generators SU(4). From these generators, a new group spin operator will be constructed. We will classify these groups into right handed groups and left handed groups. These two groups will satisfy all the properties of Pauli spin operators Sx, Sy and Sz with respect to the frame xyz. The analysis shows that the number of groups spin operators depends on the order of the group. This leads us to construct the theorem which defines the number of the groups spin operators. The analysis also leads to two kinds of frames: left handed frame (LHF) and right handed frame (RHF). The right handed operators will act on the RHF, and left hand operators act on the LHF. The study shall discuss the notion of spin squeezing for pure spin 3/2 system by using our new frames and new spin operators. It will show that our calculation is equivalent to the calculation by using Pauli spin operators.

Exact Solutions to Nonlinear Schr(?)dinger Equation and Higher-Order Nonlinear Schr(?)dinger Equation

We study solutions of the nonlinear Schroedinger equation （NLSE） and higher-order nonlinear Sehroedinger equation （HONLSE） with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method （CLGRM）, the abundant solutions of NLSE and HONLSE are obtained.

Three types of generalized Kadomtsev-Petviashvili equations arising from baroclinic potential vorticity equation

By means of the reductive perturbation method, three types of generalized （2＋l）-dimensional Kadomtsev- Petviashvili （KP） equations are derived from the baroclinic potential vorticity （BPV） equation, including the modified KP （mKP） equation, standard KP equation and cylindrical KP （cKP） equation. Then some solutions of generalized cKP and KP equations with certain conditions are given directly and a relationship between the generalized mKP equation and the mKP equation is established by the symmetry group direct method proposed by Lou et al. From the relationship and the solutions of the mKP equation, some solutions of the generalized mKP equation can be obtained. Furthermore, some approximate solutions of the baroclinic potential vorticity equation are derived from three types of generalized KP equations.

Climate and Tourism： Generational Differences and Effects on Satisfaction

Climate, weather, and its attributes such as temperature and number of rainy days are essential for the success of many tourism destinations. As climate scientists have determined that climate changes are inevitable, tourism destinations need to determine how to best manage these changes and mitigate any negative consequences. In addition, the perceived weather and/or climate at a destination can have as much weight on an individual＇s travel experience as the actual weather. The purpose of this study was to examine climate attributes and their importance on a traveler＇s behavior and satisfaction. Two hundred and sixty four surveys were gathered in the Mediterranean regions of Europe in the summer of 2009. Regression analysis revealed that climate attributes play a role in a traveler＇s satisfaction with their choice of a destination, but the traveler does not feel that climate changes are affecting their destinations as a whole. Analysis of variance （ANOVA） determined generational age differences in importance of climate attributes and if climate changes are affecting destinations. Management considerations for destination planners are explored.

Full automorphism group of the generalized symplectic graph

Let Fq be a finite field of odd characteristic, m, v the integers with 1 ≤ m ≤ v and K a 2v × 2v nonsingular alternate matrix over Fq. In this paper, the generalized symplectic graph GSp2v（q, m） relative to K over Fq is introduced. It is the graph with m-dimensional totally isotropic subspaces of the 2v-dimensional symplectic space Fq（2v） as its vertices and two vertices P and Q are adjacent if and only if the rank of PKQw is 1 and the dimension of P ∩ Q is m - 1. It is proved that the full automorphism group of the graph GSp2v（q, m） is the projective semilinear symplectic group P∑p（2v, q）.

Nowhere-zero 3-flows in Cayley graphs on generalized dihedral group and generalized quaternion group

Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero 3-flow. In this paper, we show that this conjecture is true for Cayley graph on generalized dihedral groups and generalized quaternion groups, which generalizes the result of F. Yang and X. Li [Inform. Process. Lett., 2011, 111： 416-419]. We also generalizes an early result of M. Nanasiova and M. Skoviera [J. Algebraic Combin., 2009, 30： 103-110].

Generating Relations for Grothendieck Groups of Trivial Extension Algebras

In this paper we describe explicitly the generating relations for the Grothendieck groups of trivial extension algebras of tame hereditary algebras.

Augmentation Quotients for Complex Representation Rings of Generalized Quaternion Groups

Abstract Denote by Qm the generalized quaternion group of order 4m. Let R（Qm） be its complex representation ring, and △（Qm） its augmentation ideal. In this paper, the author gives an explicit Z-basis for the △n（Qm） mid determines the isomorphism class of the n-th augmentation quotient for each positive integer n.

ON THE SHEAF OF GENERALIZED FUNDAMENTAL GROUP AND COVERING SPACE

The author constructs the sheaf of generalized fundamental group of a topological space Xand obtains the relationship between its lst cohomology set and all covering spaces Of X undersuitable conditions imposed upon X.

Coleman Automorphisms of Generalized Dihedral Groups

Let D be a generalized dihedral group and Autcol（D） its Coleman automorphism group. Denote by Outcol（D） the quotient group of Autcol（D） by Inn（D）, where Inn（D） is the inner automorphism group of D. It is proved that either Outcol（D） = i or Outcol（D） is an elementary abelian 2-group whose order is completely determined by the cardinality of π（D）. Furthermore, a necessary and sufficient condition for Outcol（D） = 1 is obtained. In addition, whenever Outcol（D） ≠ 1, it is proved that Autcol（D） is a split extension of Inn（D） by an elementary abelian 2-group for which an explicit description is given.

On Nonsingularity and Group Inverse of Linear Combinations of Generalized and Hypergeneralized Projectors

In this paper, some conditions for the nonsingularity and group inverses of linear combinations of generalized and hypergeneralized projectors are established. Moreover, some formulae for the inverses and group inverses of them are derived. The work of this paper extends some previous results.

GENERALIZED INTUITIONISTIC FUZZY HYBRID CHOQUET AVERAGING OPERATORS

In this study a new hybrid aggregation operator named as the generalized intuitionistic fuzzy hybrid Choquet averaging（GIFHCA） operator is defined.Meantime,some desirable properties are studied, and several important cases are examined.Furthermore,we define the generalized Shapley GIFHCA （GS-GIFHCA） operator,which does not only overall consider the importance of elements and their ordered positions,but also globally reflect the correlations among them and their ordered positions.In order to simplify the complexity of solving a fuzzy measure,we further define the generalizedλ-Shapley GIFHCA（GλS-GIFHCA） operator.