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.

The Power of Group Generators and Relations: An Examination of the Concept and Its Applications

This paper investigates the approach of presenting groups by generators and relations from an original angle. It starts by interpreting this familiar concept with the novel notion of “formal words” created by juxtaposing letters in a set. Taking that as basis, several fundamental results related to free groups, such as Dyck’s Theorem, are proven. Then, the paper highlights three creative applications of the concept in classifying finite groups of a fixed order, representing all dihedral groups geometrically, and analyzing knots topologically. All three applications are of considerable significance in their respective topic areas and serve to illustrate the advantages and certain limitations of the approach flexibly and comprehensively.

Average Probability of an Element Being a Generator in the Cyclic Group

All elements in the cyclic group are generated by a generator g. The number of generators of of , namely is known to be Euler’s totient function;however, the average probability of an element being a generator has not been discussed before. Several analytic properties of have been investigated for a long time. However, it seems that some issues still remain unresolved. In this study, we derive the average probability of an element being a generator using previous classical studies.

Attribution retraining group therapy for outpatients with major depression disorder,generalized anxiety disorder,and obsessive-compulsive disorder:a pilot study

The aim of this present study is to examine the efficacy of attribution retraining group therapy （ARGT） and to compare the responses of outpatients with major depression disorder （MDD）, generalized anxiety disorder （GAD） and obsessive-compulsive disorder （OCD）. We carried out a prospective uncontrolled intervention study with a 8-weeks of ARGT on sixty three outpatients with MDD, GAD or OCD. Hamilton rating scale for depression, Hamilton rating scale for anxiety, Yale-Brown obsessive-compulsive scale, attribution style questionnaire, self-esteem scale, index of well-being, and social disability screening schedule were administered before and after treatment. Significant improvement in symptoms and psychological and social functions from pre- to posttreatment occurred for all participants. The changes favored MDD patients. Our study suggested that ARGT may improve the symptoms and psychological-social functions of MDD, GAD, and OCD patients. MDD patients showed the best response.

BOUNDEDNESS OF FRACTIONAL MAXIMAL OPERATOR AND THEIR HIGHER ORDER COMMUTATORS IN GENERALIZED MORREY SPACES ON CARNOT GROUPS

In the article we consider the fractional maximal operator Mα, 0 ≤α 〈 Q on any Carnot group G （i.e., nilpotent stratified Lie group） in the generalized Morrey spaces Mp,φ（G）, where Q is the homogeneous dimension of G. We find the conditions on the pair （φ1, φ2） which ensures the boundedness of the operator Ms from one generalized Morrey space Mp,φ1 （G） to another Mq,φ2 （G）, 1. 〈 p ≤q 〈 ∞. 1/p - 1/q = α/Q, and from the space M1,φ1 （G） to the weak space Wq,φ2 （G）, 1 〈 q 〈 ∞, 1 - 1/q = α/Q. Also find conditions on the φ which ensure the Adams type boundedness of the Ms from M α （G） from Mp,φ^1/p（G）to Mq,φ^1/q（G） for 1 〈p〈q〈∞ and fromM1,φ（G） toWMq,φ^1/q（G）for 1〈q〈∞. In the case b ∈ BMO（G） and 1 〈 p 〈 q 〈 ∞, find the sufficient conditions on the pair （φ1, φ2） which ensures the boundedness of the kth-order commutator operator Mb,α,k from Mp,φ1 （G） to Mq,φ2（G） with 1/p - 1/q = α/Q. Also find the sufficient conditions on the φ which ensures the boundedness of the operator Mb,α,k from Mp,φ^1/p（G） tom Mp,φ^1/p （G） for 1 〈p〈q〈∞. In all the cases the conditions for the boundedness of Mα are given it terms of supremaltype inequalities on （φ1, φ2） and φ , which do not assume any assumption on monotonicity of （φ1, φ2） and φ in r. As applications we consider the SchrSdinger operator -△G ＋ V on G, where the nonnegative potential V belongs to the reverse Holder class B∞（G）. The MB,φ1 - Mq,φ2 estimates for the operators V^γ（-△G ＋ V）^-β and V^γ△↓G（-△G ＋ V）^-β are obtained.

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.

COMMUTATORS OF GENERALIZED HARDY OPERATORS ON HOMOGENEOUS GROUPS

Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO（G） functions on Herz spaces in the setting of homogeneous group. This article extends some known results.

Symmetry Groups and New Exact Solutions to （2＋1）-Dimensional Variable Coefficient Canonical Generalized KP Equation

In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.

Novel Mobility Formula for Parallel Mechanisms Expressed with Mobility of General Link Group

The determination of virtual constraints is always one of the key and difficult problems in traditional mobility calculation. To make mobility calculation simple, considering avoiding virtual constraints, some new formulae have been presented, however these formulae can hardly intuitively reflect general link group＇s restrictions on output member and its influences on independence of output parameters, which is premise to the judgment of the properties of mobility. Towards the problem to reveal the intrinsic relationship between the degree of freedom（DOF） of a mechanism, the link group, and the dimension of output parameters, also to avoid determination of virtual constraint, based on the new concepts of the ＂DOF of general link group＂ and ＂node parameters＂, a new formula in the calculation of the mobility of mechanisms is presented that is expressed with DOFs of the general link groups and rank of motion parameters of base point of the output link. It is named GOM（mobility of groups and output parameter） formula. On the basis of new concepts of＂effective parameters＂ and ＂invalid parameters＂, a rule is put forward for solving the DOF of mechanisms with invalid parameters by GOM formula, that is, the base point parameters are the subset of effective parameters of link group. Thereafter, several examples are enumerated and the results coincide with the prototype data, which proves the validity of the proposed formula. Meanwhile, it is obtained that the necessary and sufficient condition for the judgment of output parameters independence is that each of the DOF of the link group is not less than zero. The proposed formula which is simple in calculation provides theoretical basis for the judgment of independence of output parameters and provides references for type synthesis of novel parallel mechanisms with independence requirements of their output parameters.

Growth performance and physiological parameters of the second generation selected and control groups of Pinctada martensii

In May of 2007,the second generation selected （SS） and control （SC） groups of pearl oyster Pinctada martensii were established by selecting 10% breeders with the largest and mean shell length,respectively,from the first generation selected group.Growth performance of the SS and SC groups were compared on the basis of measurement data at Days 8,18,60,95,195 and 365.On Day 365,100 individuals （60.0–75.0 mm at shell length） were sampled from each group and then subjected to the experiment where physiological parameters such as filtrate rate,oxygen consumption and ammonia excretion were measured at 15,20,25 and 30°C.The results show that the SS group had significantly larger mean shell length and shell height than the SC group at Days 8,18,60,95,195 and 365 （P 0.05）.The genetic gains at different ages varied from 6.0% to 17.0% for shell length and 5.7% to 14.6% for shell height,respectively.At 15,20,25 and 30 ° C,the SS groups had significantly larger filtrate rate than the SC group （P 0.05）.At 15 and 25 °C,the differences in oxygen consumption rate between the SS and SC groups were not significant （P 0.05）.At 20 and 30 °C,however,the oxygen consumption rate of the SS group was significantly larger than the SC group （P 0.05）.At 15,20,25 and 30 °C,there were no significant differences in ammonia excretion rate between the SS and SC groups （P 0.05）.The present results indicate that there existed considerable genetic variability in the base population and a further selection could be likely fruitful.Mass selection for faster growth might produce animals that had higher intake of metabolizable energy by virtue of faster filtrating behavior.

Symmetry and general symmetry groups of the coupled Kadomtsev-Petviashvili equation

In this paper, the Lie symmetry algebra of the coupled Kadomtsev-Petviashvili （cKP） equation is obtained by the classical Lie group method and this algebra is shown to have a Kac-Moody-Virasoro loop algebra structure. Then the general symmetry groups of the cKP equation is also obtained by the symmetry group direct method which is proposed by Lou et alo From the general symmetry groups, the Lie symmetry group can be recovered and a group of discrete transformations can be derived simultaneously. Lastly, from a known simple solution of the cKP equation, we can easily obtain two new solutions by the general symmetry groups.

GENERALIZED INVERSE GROUP OF SIGNAL AND ITS IMPLEMENTATION WITH NEURAL NETWORKS

A new concept, the generalized inverse group (GIG) of signal, is firstly proposed and its properties, leaking coefficients and implementation with neural networks are presented. Theoretical analysis and computational simulation have shown that (1) there is a group of finite length of generalized inverse signals for any given finite signal, which forms the GIG; (2) each inverse group has different leaking coefficients, thus different abnormal states; (3) each GIG can be implemented by a grouped and improved single-layer perceptron which appears with fast convergence. When used in deconvolution, the proposed GIG can form a new parallel finite length of filtering deconvolution method. On off-line processing, the computational time is reduced to O(N) from O(N2). And the less the leaking coefficient is, the more reliable the deconvolution will be.

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.

On (2, 3, <i>t</i>)-Generations for the Rudvalis Group Ru

A group G is said to be(2,3,t) -generated if it can be generated by an involution x and an element y so that 0(y)=3?and 0(xy)=t. In the present article, we determine all (2,3,t)-generations for the Rudvalis sporadic simple group Ru, where t is any divisor of .

LIE GROUP INTEGRATION FOR CONSTRAINED GENERALIZED HAMILTONIAN SYSTEM WITH DISSIPATION BY PROJECTION METHOD

For the constrained generalized Hamiltonian system with dissipation, by introducing Lagrange multiplier and using projection technique, the Lie group integration method was presented, which can preserve the inherent structure of dynamic system and the constraint-invariant. Firstly, the constrained generalized Hamiltonian system with dissipative was converted to the non-constraint generalized Hamiltonian system, then Lie group integration algorithm for the non-constraint generalized Hamiltonian system was discussed, finally the projection method for generalized Hamiltonian system with constraint was given. It is found that the constraint invariant is ensured by projection technique, and after introducing Lagrange multiplier the Lie group character of the dynamic system can't be destroyed while projecting to the constraint manifold. The discussion is restricted to the case of holonomic constraint. A presented numerical example shows the effectiveness of the method.

On the Power Performance of Test Statistics for the Generalized Rayleigh Interval Grouped Data

In this paper, the weighted Kolmogrov-Smirnov, Cramer von-Miss and the Anderson Darling test statistics are considered as goodness of fit tests for the generalized Rayleigh interval grouped data. An extensive simulation process is conducted to evaluate their controlling of type 1 error and their power functions. Generally, the weighted Kolmogrov-Smirnov test statistics show a relatively better performance than both, the Cramer von-Miss and the Anderson Darling test statistics. For large sample values, the Anderson Darling test statistics cannot control type 1 error but for relatively small sample values it indicates a better performance than the Cramer von-Miss test statistics. Best selection of the test statistics and highlights for future studies are also explored.

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.

Group of Weakly Continuous Operators Associated to a Generalized Schrödinger Type Homogeneous Model

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger type homogeneous model in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a group of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we give some remarks derived from this study.

Hierarchical Merging &Generalization Method of Three-Dimension City Model Group Based on the Theory of Spatial Visual Cognition

In order to simplify the three-dimensional building group model, this paper proposes a clustering generalization method based on visual cognitive theory. The method uses road elements to roughly divide scenes, and then uses spatial cognitive elements such as direction, area, height and their topological constraints to classify them precisely, so as to make them conform to the urban morphological characteristics. Delaunay triangulation network and boundary tracking synthesis algorithm are used to merge and summarize the models, and the models are stored hierarchically. The proposed algorithm should be verified experimentally with a typical urban complex model. The experimental results show that the efficiency of the method used in this paper is at least 20% higher than that of previous one, and with the growth of test data, the higher efficiency is improved. The classification results conform to human cognitive habits, and the generalization levels of different models can be relatively unified by adaptive control of each threshold in the clustering generalization process.

Designing a Protection Scheme in Micro-Grid Systems with DG Using Central Protection Unite and Multiple Setting Group Protection Relays

Distributed generators now is widely used in electrical power networks, in some cases it works seasonally, and some types works at special weather conditions like photo voltaic systems and wind energy, and due to this continuous changes in generation condition, the fault current level in network will be affected, this changes in fault current level will affect in the coordination between protection relays and to keep the coordination at right way, an adaptive protection system is required that can adaptive its setting according to generation changes, the fault current level in each case is evaluated using ETAP software, and the required relay setting in each case is also evaluated using Grey Wolf Optimizer (GWO) algorithm, and to select suitable setting which required in each condition, to select the active setting group of protection relay according to generation capacity, central protection unite can be used, and to improve protection stability and minimizing relays tripping time, a proposed method for selecting suitable backup relay is used, which leads to decrease relays tripping time and increase system stability, output settings for relays in all cases achieved our constrains.