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We show that inSU(3) C ×SU(3) L ×U(1) X model, the leading contribution to the electric and chromolelectric dipole moment of the top quark is due to the one-loop diagrams which come from exchanging the charged and neutral Higgs bosons. The dipole moments are typically of the order of 10−19 e-cm and 10−19 g-cm respectively, for the values of relative phases of the vev's such that CP violation is maximal. From an experimental point of view, theq 2 dependence of dipole moment form factors is given.

In this note, we compute the virtual first Betti numbers of 4-manifolds fibering over $S^1$ with prime fiber. As an application, we show that if such a manifold is symplectic with nonpositive Kodaira dimension, then the fiber itself is a sphere or torus bundle over $S^1$. In a different direction, we prove that if the 3-dimensional fiber of such a 4-manifold is virtually fibered then the 4-manifold is virtually symplectic unless its virtual first Betti number is 1., Comment: 17 pages

We diagonalize the mass matrix of Higgs bosons and obtain its eigenvalues and eigenstates in the SU(3)[sub [ital c]][times]SU(3)[sub [ital L]][times]U(1)[sub [ital X]] model. We estimate in detail the size of the electric dipole moment [ital d][sub [ital W]] of the [ital W] boson which comes from exchanging neutral and charged Higgs bosons in this model. [ital d][sub [ital W]] remains within the present upper bound of 10[sup [minus]20][ital e] cm, even for the values of relative phases of the VEV's such that [ital CP] violation is maximal.

For a compact almost complex 4-manifold $(M,J)$, we study the subgroups $H^{\pm}_J$ of $H^2(M, \mathbb{R})$ consisting of cohomology classes representable by $J$-invariant, respectively, $J$-anti-invariant 2-forms. If $b^+ =1$, we show that for generic almost complex structures on $M$, the subgroup $H^-_J$ is trivial. Computations of the subgroups and their dimensions $h^{\pm}_J$ are obtained for almost complex structures related to integrable ones. We also prove semi-continuity properties for $h^{\pm}_J$., Comment: 30 pages

In this note we show that the Lagrangian Luttinger surgery preserves the symplectic Kodaira dimension. Some constraints on Lagrangian tori in symplectic four manifolds with non-positive Kodaira dimension are also derived., Comment: 23 pages; to appear in Asian Journal of Mathematics

Given a Lagrangian sphere in a symplectic 4-manifold $(M, \omega)$ with $b^+=1$, we find embedded symplectic surfaces intersecting it minimally. When the Kodaira dimension $\kappa$ of $(M, \omega)$ is $-\infty$, this minimal intersection property turns out to be very powerful for both the uniqueness and existence problems of Lagrangian spheres. On the uniqueness side, for a symplectic rational manifold and any class which is not characteristic and ternary, we show that homologous Lagrangian spheres are smoothly isotopic, and when the Euler number is less than 8, we generalize Hind and Evans' Hamiltonian uniqueness in the monotone case. On the existence side, when $\kappa=-\infty$, we give a characterization of classes represented by Lagrangian spheres, which enables us to describe the non-Torelli part of the symplectic mapping class group.

In this note we introduce the notion of the relative symplectic cone. As an application, we determine the symplectic cone of certain T^2-fibrations. In particular, for some elliptic surfaces we verify a conjecture on the symplectic cone of minimal Kaehler surfaces raised by the second author.

To evaluate the therapeutic effects of galvanism penetration of traditional Chinese medicine combined with ultrasonic wave and manipulation in the treatment of strain of the infrapatellar fat pad, to study an effective approach in the treatment of this diseas.Eighty patients were divided randomly into treatment group and control group, there were 40 cases in each group. In treatment group 40 cases were treated by galvanism penetration of traditional Chinese medicine, ultrasonic wave and manipulation, included 22 males and 18 females with an average age of (63.15 +/- 8.10) years old and a mean disease course of (6.84 +/- 3.50) years. In control group, 40 cases were treated with ultrasonic wave and manipulation, included 23 males and 17 females with an average age of (62.63 +/- 8.20) years old and the course was (6.59 +/-3.70) years. visual analogue scale (VAS) and the scales for pain with finger press were evaluated before and after treatment in two groups. The clinical effects were researched and analysed statistically.In treatment group,12 patients were in remarkable effects, 17 in good effective, 9 in effective and 2 in ineffective. As well in control group, above data were 8,15, 8 and 9 respectively. There was a significant difference in the rate of general effective between treatment group and control group (P0.05). In treatment group, the scales for VAS before and after treatment were (7.92 +/- 2.21) and (2.16 +/- 1.87) and the scales for pain with finger press before and after treatment were (3.01 +/- 0.63) and (0.86-- 0.46). As well in control group, above data were (7.71 +/2.65), (3.83 +/- 2.45), (2.98 +/- 0.61) and (1.32 +/- 0.52) respectively. The comparison of the scales for VAS and pain with finger press before and after treatment in two groups had significant difference (PO.01).Ultrasonic wave and manipulation have a good effect in the treatment of stain of the infrapatellar fat pad, when the galvanism penetration of traditional Chinese medicine is applied at the same time, the therapeutic efficiency can be improved significantly. Three therapies are used in treatment at the same, it can improve the therapeutic effect, and it is an easy, economic, practical and effective comprehensive approach.

We define relative Ruan invariants that count embedded connected symplectic submanifolds which contact a fixed symplectic hypersurface V in a symplectic 4-manifold (X, ω) at prescribed points with prescribed contact orders (in addition to insertions on X\V). We obtain invariants of the deformation class of (X, V, ω). Two large issues must be tackled to define such invariants: (1) curves lying in the hypersurface V and (2) genericity results for almost complex structures constrained to make V pseudo-holomorphic (or almost complex). Moreover, these invariants are refined to take into account rim-tori decompositions. In the latter part of the paper, we extend the definition to disconnected submanifolds and construct relative Gromov–Taubes invariants.

For any compact almost complex manifold (M, J), the last two authors [8] defined two subgroups H + J (M), H − J (M) of the degree 2 real de Rham cohomology group . These are the sets of cohomology classes which can be represented by J-invariant, respectively, J-antiinvariant real 2-forms. In this paper, it is shown that in dimension 4 these subgroups induce a cohomology decomposition of . This is a specifically four-dimensional result, as it follows from a recent work of Fino and Tomassini [6]. Some estimates for the dimensions of these groups are also established when the almost complex structure is tamed by a symplectic form and an equivalent formulation for a question of Donaldson is given.

In this paper we show that every degree 2 homology class of a 2n-dimensional symplectic manifold is represented by an immersed symplectic surface if it has positive symplectic area. Moreover, the symplectic surface can be chosen to be embedded if 2n is at least 6. We also analyze the additional conditions under which embedded symplectic representatives exist in dimension 4.

To observe the effect platelet antigen modification by mPEG-SPA with different molecular masses.Platelet CD42a was modified by 5 kD and 20 kD mPEG-SPA, respectively, and the fluorescence intensity of CD42a was detect by flow cytometry and the three-dimensional structure of CD42a simulated to analyze the distribution of lysine in CD42a molecule.After platelet CD42a modification by 5 kD and 20 kD mPEG-SPA, the fluorescence intensity of CD42a decreased sharply by 85.54% and 88.65%, respectively, and multiple lysine regions were identified on the surface of CD42a molecule.Both 5 kD and 20 kD mPEG-SPA allow useful modification of platelet CD42a, but 20 kD mPEG-SPA is more advantageous than 5 kD mPEG-SPA.

We introduce certain homology and cohomology subgroups for any almost complex structure and study their pureness, fullness and duality properties. Motivated by a question of Donaldson, we use these groups to relate J-tamed symplectic cones and J-compatible symplectic cones over a large class of almost complex manifolds, including all Kahler manifolds, almost Kahler 4-manifolds and complex surfaces., Comment: v3 substantially revised and title changed, v4 One main result (Theorem 1.3) substantially improved

A symplectic manifold $(M,\omega)$ is called {\em (symplectically) uniruled} if there is a nonzero genus zero GW invariant involving a point constraint. We prove that symplectic uniruledness is invariant under symplectic blow-up and blow-down. This theorem follows from a general Relative/Absolute correspondence for a symplectic manifold together with a symplectic submanifold. A direct consequence is that symplectic uniruledness is a symplectic birational invariant. Here we use Guillemin and Sternberg's notion of cobordism as the symplectic analogue of the birational equivalence., Comment: To appear in Invent. Math

We discuss the notion of the Kodaira dimension for symplectic manifolds in dimension 4. In particular, we propose and partially verify Betti number bounds for symplectic 4-manifolds with Kodaira dimension zero.

We introduce an analogue of the inflation technique of Lalonde-McDuff, allowing us to obtain new symplectic forms from symplectic surfaces of negative self-intersection in symplectic four-manifolds. We consider the implications of this construction for the symplectic cones of K\"ahler surfaces, proving along the way a result which can be used to simplify the intersections of distinct pseudoholomorphic curves via a perturbation., Comment: 17 pages. To appear in Journal of Symplectic Geometry

Let $A(M)$ be the automorphism group of the middle homology of a smooth 4-manifold $M$ and $D(M)$ be the subgroup induced by diffeomorphisms of $M$. In this paper we give explicit generators of $D(M)$ for rational and ruled 4-manifolds. We also prove the uniqueness of reduced forms for classes with minimal genus 0 and non-negative square.

The Kodaira dimension of a non-minimal manifold is defined to be that of any of its minimal models. It is shown in [12] that, if ω is a Kahler form on a complex surface (M,J), then κ(M,ω) agrees with the usual holomorphic Kodaira dimension of (M,J). It is also shown in [12] that minimal symplectic 4−manifolds with κ = 0 are exactly those with torsion canonical class, thus can be viewed as symplectic Calabi-Yau surfaces. Known examples of symplectic 4−manifolds with torsion canonical class are either Kahler surfaces with (holomorphic) Kodaira dimension zero or T 2−bundles over T 2 ([10], [12]). They all have small Betti numbers and Euler numbers: b+ ≤ 3, b ≤ 19 and b1 ≤ 4; and the Euler number is between 0 and 24. It is speculated in [12] that these are the only ones. In this paper we prove that it is true up to rational homology.

The geography problem is usually stated for simply connected symplectic 4-manifolds. When the first cohomology is nontrivial, however, one can restate the problem taking into account how close the symplectic manifold is to satisfying the conclusion of the Hard Lefschetz Theorem, which is measured by a nonnegative integer called the degeneracy. In this paper we include the degeneracy as an extra parameter in the geography problem and show how to fill out the geography of symplectic 4-manifolds with Kodaira dimension 1 for all admissible triples., Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-15.abs.html

Let M be a closed oriented smooth 4-manifold admitting symplectic structures. If M is minimal and has b+ = 1, we prove that there is a unique symplectic canonical class up to sign, and any real second cohomology class of positive square is represented by symplectic forms. Similar results hold when M is not minimal.

In this paper, the symplectic genus for any 2-dimensional class in a 4-manifold admitting a symplectic structure is introduced, and its relation with the minimal genus is studied. It is used to describe which classes in rational and irrational ruled manifolds are realized by connected symplectic surfaces. In particular, we completely determine which classes with square at least -1 in such manifolds can be represented by embedded spheres. Moreover, based on a new characterization of the action of the diffeomorphism group on the intersection forms of a rational manifold, we are able to determine the orbits of the diffeomorphism group on the set of classes represented by embedded spheres of square at least -1 in any 4-manifold admitting a symplectic structure., Comment: 28 pages

We discuss dilaton and Moduli dominant SUSY breaking scenarios in M-theory. In addition, for the nonperturbative superpotential from gaugino condensation, we discuss the soft terms in the simplest model (only S and T moduli fields) and in the $T^6/Z_{12}$ model from M-theory. From the phenomenology consideration, we suggest massless scalar SUSY breaking scenario., Comment: 15 pages, latex, 4 figures

Lefschetz fibration is the symplectic analogue of stable holomorphic fibration in complex geometry. A 4-dimensional stable holomorphic fibration satisfies the famous Parshin-Arakelov inequality. In this note we present an analogous inequality for a 4-dimensional Lefschetz fibration.

).In the series of works [T1]–[T4];Taubes develops the Seiberg-Witten theory onsymplectic manifolds. In [T1];he defines the Gromov-Taubes invariants of symplectic4-manifolds counting embedded (but not necessarily connected);pseudoholomorphiccurves. (It was recently proved in [EP] that the Gromov invariants can also be constructedfrom the Ruan-Tian invariants [RT2]). In [T2];[T3];and [T4];Taubes proves;on a sym-plectic 4-manifold with b

In this paper, we present some calculation of the Gromov–Witten invariants of S2 × T 2. Since the symplectic Gromov–Witten invariants in fact only depend on the deformation class of symplectic forms and we have shown in [10] that there is a unique deformation class on S2 ×T 2, we merely need to compute the Gromov–Witten invariants for some specific symplectic structure. We will actually pick some Kahler structures in the computation. Let (M,ω) be a symplectic S2 × T 2 and [S2] and [T 2] be the homology classes represented by S2 × pt and pt × T 2, respectively, and pair positively with the symplectic form ω. Denote the homology class l[S2]+d[T 2] by Al,d and we simply write A1,d as Ad . Our first result is about the embedded genus one curves of the sequence of classes Al,1. More precisely, let us define N1(Al,1) as the number of embedded genus 1 curves in the class A1,d and passing through 2l points.