Lie symmetry group transformation for MHD natural convection flow of nanofluid over linearly porous stretching sheet in presence of thermal stratification

The magnetohydrodynamics （MHD） convection flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the pres- ence of thermal stratification are examined. The partial differential equations governing the problem under consideration are transformed by a special form of the Lie symmetry group transformations, i.e., a one-parameter group of transformations into a system of ordinary differential equations which are numerically solved using the Runge-Kutta-Gill- based shooting method. It is concluded that the flow field, temperature, and nanoparticle volume fraction profiles are significantly influenced by the thermal stratification and the magnetic field.

Lie point symmetry algebras and finite transformation groups of the general Broer-Kaup system

Using a new symmetry group theory, the transformation groups and symmetries of the general Broer-Kaup system are obtained. The results are much simpler than those obtained via the standard approaches.

ALMOST PERIODICITY AND EQUICONTINUITY OF THE TOPOLOGICAL TRANSFORMATION GROUP

In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.

Finite symmetry transformation group and localized structures of the (2+1)-dimensional coupled Burgers equation

In this paper, the finite symmetry transformation group of the （2＋1）-dimensional coupled Burgers equation is studied by the modified direct method, and with the help of the truncated Painleve′ expansion approach, some special localized structures for the （2＋1）-dimensional coupled Burgers equation are obtained, in particular, the dromion-like and solitoff-like structures.

APPLICATION OF ONE-PARAMETER GROUPS OF TRANSFORMATION IN MECHANICS

In this paper,including some partial differential equations with a number of independent variables, which can he reduced by the infinitesimal form of the group, we obtain the theory of similarity transformation and its application of the second order nonlinear partial differential equations which have two independent variables and two dependent variables in mechanics.

Noether Symmetry Can Lead to Non-Noether Conserved Quantity of Holonomic Nonconservative Systems in General Lie Transformations

For the holonomic nonconservative system, by using the Noether symmetry, a non-Noether conserved quantity is obtained directly under general infinitesimal transformations of groups in which time is variable. At first,the Noether symmetry, Lie symmetry, and Noether conserved quantity are given. Secondly, the condition under which the Noether symmetry is a Lie symmetry under general infinitesimal transformations is obtained. Finally, a set of nonNoether conserved quantities of the system are given by the Noether symmetry, and an example is given to illustrate the application of the results.

On fundamental solution for powers of the sub-Laplacian on the Heisenberg group

We discuss the fundamental solution for m-th powers of the sub-Laplacian on the Heisenberg group. We use the representation theory of the Heisenberg group to analyze the associated m-th powers of the sub-Laplacian and to construct its fundamental solution. Besides, the series representation of the fundamental solution for square of the sub-Laplacian on the Heisenberg group is given and we also get the closed form of the fundamental solution for square of the sub-Laplacian on the Heisenberg group with dimension n = 2, 3, 4.

Preliminary group classification of quasilinear third-order evolution equations

Group classification of quasilinear third-order evolution equations is given by using the classical infinitesimal Lie method, the technique of equivalence transformations, and the theory of classification of abstract low-dimensional Lie algebras. We show that there are three equations admitting simple Lie algebras of dimension three. All non-equivalent equations admitting simple Lie algebras are nothing but these three. Furthermore, we also show that there exist two, five, twenty-nine and twenty-six non- equivalent third-order nonlinear evolution equations admitting one-, two-, three-, and four-dimensional solvable Lie algebras, respectively.

WAVELET TRANSFORM ASSOCIATED TO THE AFFINE GROUP AGS,

This paper considers wavelet transforms associated to the affine group, which is more general than the paper given by R. Murenzi, and it seems more important in mathematical theory and more natural to be used to analyze signals in more than 1-dimension.

Parameter Estimations of Rayleigh Distribution

设随机变量X服从Rayleigh分布，其密度函数为p(x;β)=2x/βe-x^2/β，x＞0,β＞0为参数，对变换群G={gc;gc(x)=c^2x,c＞0}，本文分别在平方损失和熵损失下研究了β在G上的最优同变估计；当β有先验信息时，给出了β的Bayes估计。

Effects of slip condition on MHD stagnation-point flow over a power-law stretching sheet

The steady two-dimensional magnetohydrodynamic stagnation flow towards a nonlinear stretching surface is studied. The no-slip condition on the solid boundary is replaced with a partial slip condition. A scaling group transformation is used to get the invariants. Using the invariants, a third-order ordinary differential equation corresponding to the momentum is obtained. An analytical solution is obtained in a series form using a homotopy analysis method. Reliability and efficiency of series solutions are shown by the good agreement with numerical results presented in the literature. The effects of the slip parameter, the magnetic field parameter, the velocity ratio parameter, the suction velocity parameter, and the power law exponent on the flow are investigated. The results show that the velocity and shear stress profiles are greatly influenced by these parameters.

SIMILARITY SOLUTION OF SELF-WEIGHT CONSOLIDATION PROBLEM FOR SATURATED SOIL

A more general assumption than that in the classical one-dimensional large strain consolidation theory is adopted and the exact analytical solution of nonlinear finite strain self-weight consolidation based on this assumption is obtained. By applying the same experimental data, the comparison of the solutions of linear and nonlinear finite strain theory, as well as the numerical calculating results based on finite element method is presented. The results of the comparison show that the analytical solution obtained here takes on better agreement with practical cases than that of linear one, and they also show that, compared with the solutions based on nonlinear theory, the settlement and the consolidation degree based on linear theory are smaller.

Generalized covariant differentiation and axiom-based tensor analysis

This paper reports the new progresses in the axiomatization of tensor anal- ysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomatized definition, the algebraic structure, the transformation group, and the simple calculation of generalized covariant differentia- tions. These progresses strengthen the tendency of the axiomatization of tensor analysis.

Extension of covariant derivative(Ⅲ): From classical gradient to shape gradient

This paper further extends the generalized covari ant derivative from the first covariant derivative to the sec ond one on curved surfaces. Through the linear transforma tion between the first generalized covariant derivative and the second one, the second covariant differential transformation group is set up. Under this transformation group, the sec ond class of differential invariants and integral invariants on curved surfaces is made clear. Besides, the symmetric struc ture of the tensor analysis on curved surfaces are revealed.

Extension of covariant derivative(Ⅱ): From flat space to curved space

This paper extends the classical covariant deriva tive to the generalized covariant derivative on curved sur faces. The basement for the extension is similar to the pre vious paper, i.e., the axiom of the covariant form invariabil ity. Based on the generalized covariant derivative, a covari ant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analy sis on curved surfaces is simplified intensively. Under the covariant differential transformation group, the differential invariabilities and integral invariabilities are constructed on curved surfaces.

Telechelic Triblock Poly(α-Amino Acid)-Poly(Tetrahydrofuran)-Poly(α-Amino Acid)Copolymers:Chain-End Transformation,Polymerization and pH-Responsive Hydrolysis

Main observation and conclusion Block copolymers not only combine properties of different segments but also generate new application prospects.Poly(α-amino acid)-b-poly(tetrahydrofuran)-b-poly(α-amino acid)(PAA-PTHF-PAA)is one of the copolymers.In this contribution,di-hydroxyl-ended HO-PTHF-OH is transferred into di-oxyamino-ended H2NO-PTHF-ONH2 quantitatively,which is used as a macroinitiator to polymerize sarcosine N-thiocarboxyanhydride(Sar-NTA)and N-phenyoxycarbonyl N-ε-carbobenzyloxy-D-lysine(ZDL-NPC).Well-defined triblock PAA-NHO-PTHF-ONH-PAA is produced with high molecular weight(up to 25.3 kg/mol)and narrow dispersity.The amphiphilic PSar-NHO-PTHF-ONH-PSar(STS)self-assembles into micelles with uniform diameters of 30—40 nm according to DLS.Owing to oxygen amide groups inside the backbone of these copolymers,the polyether-poly(amino acid)s block copolymers are cleavable under an acidic environment and therefore have potential applications in smart biomedicine and engineering.

Estimates of the Isovariant Borsuk–Ulam Constants of Connected Compact Lie Groups

The isovariant Borsuk Ulam constant cc of a compact Lie group G is defined to be the supremum of c ∈ R such that the inequalityc（dim V - dim V^C） ≤ dim W - dim W^Gholds whenever there exists a G-isovariant map f ： S（V） → S（W） between G-representation spheres. In this paper, we shall discuss some properties of cG and provide lower estimates of cG of connected compact Lie groups, which leads us to some Borsuk-Ulam type results for isovariant maps. We also introduce and discuss the generalized isovariant Borsuk-Ulam constant c^-G for more general smooth G-actions on spheres. The result is considerably different from the case of linear actions.

Simultaneous ISAR imaging of group targets flying in formation

This paper proposes a novel inverse synthetic aperture radar（ISAR） imaging method based on second-order keystone transform（KT） and Sandglass transform for group targets flying in a formation with constant accelerated rectilinear motion in the same radar beam. First, range curvature and range walk of each sub-target among group targets are corrected by the second-order KT combined with the quadratic phase term compensation. After range alignment, the signals in each range frequency cell can be modelled as multiple chirp signals and then the Sandglass transform is utilized to cross-range imaging, which transforms the time–frequency distribution of the signals in each range frequency cell into beelines parallel to the slow time axis simultaneously. Finally, cross-range profiles of group targets in each range frequency cell are obtained via a projection of the perk of every scatterer in the two-dimensional accumulation plane onto the frequency axis. The advantage of the proposed method is that it can align range profiles of each sub-target simultaneously and image cross-range profiles directly without separating the returned signals, which simplifies the operation procedure. Simulation results are used to demonstrate the effectiveness of the proposed method.

New Generalizations of Migdal-Kadanoff Bond-Moving Recursion Procedures and Their Applications

Considering in symmetrical half-length bond operations,we present in this paper two types of newlydeveloped generalizations of the remarkable Migdal-Kadanoff bond-moving renormalization group transformation recursion procedures.The predominance in application of these generalized procedures are illustrated by making use of them to study the critical behavior of the spin-continuous Gaussian model constructed on the typical translational invariant lattices and fractals respectively.Results such as the correlation length critical exponents obtained by these means are found to be in good conformity with the classical results from other previous studies.

Mbius Homogeneous Hypersurfaces with Three Distinct Principal Curvatures in S^(n+1)

Let x ： M^n→S^n＋1 be an immersed hypersurface in the （n ＋1）-dimensional sphere S^n＋1. If, for any points p,q ∈ M^n, there exists a Mobius transformation Ф ： S^n＋l →S^n＋1 such that Ф o x（M^n） = x（M^n） and Ф o x（p） = x（q）, then the hypersurface is called a Mobius homogeneous hypersurface. In this paper, the Mobius homogeneous hypersurfaces with three distinct principal curvatures are classified completely up to a Mobius transformation.