Orthomodular Lattices and Quantales

Let L be a complete orthomodular lattice. There is a one to one correspondence between complete Boolean subalgebras of L contained in the center of L and endomorphisms j of L satisfying the Borceux–van den Bossche conditions. This article is dedicated to Raquel Hernández. SUBJCLASS: 0210.Ab, 0210.De, 03.65.-ca     

大视场双目头盔投影光学系统设计

设计了一种新型的头盔投影光学系统,解决了头盔系统中大视场和双目实现之间的设计矛盾,且有较小的重量和尺寸.系统的特性参量为：视场角60°,有效焦距30 mm,出瞳距离25 mm,出瞳直径12 mm.该系统由折/衍混合双高斯镜头、半透半反镜和回射屏组成.像差分析结果表明,系统的最大像散为0.27 mm,垂轴色差小于2.7 μm,畸变小于3.8%,最小分辨角为0.5 mrad,成像质量高.     

Characterization of Morita Equivalence Pairs of Quantales

We characterize the pairs of sup-lattices which occur as pairs of Morita equivalence bimodules between quantales in terms of the mutual relation between the sup-lattices.     

Some Remarks on Special Conformal and Special Projective Symmetries in General Relativity

Those space-times admitting special conformal vector fields and those admitting special projective vector fields have recently been studied. In this paper these two classes of space times are shown to be very closely related to each other. Certain uniqueness features of (and necessary extra symmetries contained in) the associated Lie algebras are discussed and the dimensionality of each of the algebras is computed.     

New Exact Travelling Wave Solutions for Generalized Zakharov-Kuzentsov Equations Using General Projective Riccati Equation Method

Applying the generalized method, which is a direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer algebraic system, we consider the generalized Zakharov-Kuzentsov equation with nonlinear terms of any order. As a result, we can not only successfully recover the previously known travelling wave solutions found by existing various tanh methods and other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shaped solitons, bell-shaped solitons, singular solitons, and periodic solutions.     

Plasma Applications: A Dermatological View

The ability to produce cold plasma at atmospheric pressure conditions was the basis for the rapid growth of plasma related application areas in biomedicine. Plasma comprises a multitude of active components such as charged particles, electric current, UV radiation, and reactive species which can act synergistically. The antiitch, antimicrobial, and anti‐inflammatory effect was already demonstrated in in vivo and in vitro experiments and until now no resistance of pathogens against plasma treatment was observed. The combination of the different active agents and their broad range of positive effects on various diseases, especially easily accessible skin diseases, render plasma quite attractive for applications in medicine. Hence, plasma medicine as an independent and promising medical field has been emerged recently. For medical applications two different types of cold plasma are suitable; indirect (plasma jet, plasma torch) and direct plasma sources (dielectric barrier discharge ‐ DBD). So far, no standards and norms are defined for any of these plasma sources. Also, no convenient criteria for standardization of the quality rating of plasma in the view of dermatological applications exist. Although various cold plasma studies have been performed the results are hardly comparable, as physical parameters of the plasma devices, experimental conditions, and organisms used vary greatly. Therefore, standardized risk analyses are necessary for the assessment of different plasma sources. In this review two plasma sources are described and possible risk factors are discussed to estimate the safety of plasma used as a therapeutic tool in dermatology. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Morita Contexts and their Lattices of Relations

We study the interaction between the lattices of relations of members of a general Morita context. The pairs of reversing-order maps are defined, which determine the dualities between the lattices of ‘closed’ relations. Under rather weak conditions, these dualities can be composed obtaining the projectivities defined by simple maps. PACS: 02.10.De,02.10.Hh.     

Projective differential geometry and geodesic conservation laws in general relativity. I: Projective actions

The Lagrangian structure of the geodesic equation allows an extension of classical projective geometry to one-parameter projective group actions onR×TM (whereM is the spacetime). We determine all those projective actions which arise by prolongation of oneparameter group actions onR×M. The relation between projective actions onR×TM and the equation of geodesic deviation is developed.     

A Quantization on Riemann Surfaces with Projective Structure

Let X be a Riemann surface equipped with a projective structure. Let be a square-root of the holomorphic cotangent bundle K _X . Consider the symplectic form on the complement of the zero section of obtained by pulling back the symplectic form on K _X using the map ². We show that this symplectic form admits a natural quantization. This quantization also gives a quantization of the complement of the zero section in K _X equipped with the natural symplectic form.     

Projective Relativity: Present Status and Outlook

We give a critical analysis of projective relativity theory. Examining Kaluza's own intention and the following development by Klein, Jordan, Pauli, Thiry, Ludwig and others, we conclude that projective relativity was abused in its own terms and much more in the case of newer higher dimensional Kaluza–Klein theories with non-Abelian gauge groups. Reviewing the projective formulation of the Jordan isomorphy theorem yields some hints how one can proceed in a different direction. We can interpret the condition not as a field equation in a 5-dimensional Riemannian space, e.g. as vacuum Einstein-Hilbert equation, but can (or should) interpret it as a geometrical object, a null-quadric. Projective aspects of quantum (field) theory are discussed under this viewpoint.     

Projective quantum spaces

Associated to the standard SU _q (n) R-matrices, we introduce quantum spheresS _q ^2n-1 , projective quantum spaces _q ^n-1 , and quantum Grassmann manifoldsG _k( _q ⁿ ). These algebras are shown to be homogeneous spaces of standard quantum groups and are also quantum principle bundles in the sense of T. Brzeziski and S. Majid.     

Disentangling q-Exponentials: A General Approach

We revisit the q-deformed counterpart of the Zassenhaus formula, expressing the Jackson q-exponential of the sum of two non-q-commuting operators as an (in general) infinite product of q-exponential operators involving repeated q-commutators of increasing order, E_q(A+B) = E_q0(A)E_q1 (B) _i=2 E_qi. By systematically transforming the q-exponentials into exponentials of series and using the conventional Baker–Campbell–Hausdorff formula, we prove that one can make any choice for the bases ^qi, i=0, 1, 2, ..., of the q-exponentials in the infinite product. An explicit calculation of the operators C _i in the successive factors, carried out up to sixth order, also shows that the simplest q-Zassenhaus formula is obtained for ₀ = ₁ =1, and ₂ = 2, and ₃ = 3. This confirms and reinforces a result of Sridhar and Jagannathan, on the basis of fourth-order calculations.     

A Criterion for Compatibility of Conformal and Projective Structures

In a space-time M, a conformal structure is defined by the distribution of light-cones. Geodesics are traced by freely falling particles, and the collection of all unparameterized geodesics determines the projective structure of M. The article contains a formulation of the necessary and sufficient conditions for these structures to be compatible, i.e. to come from a metric tensor which is then unique up to a constant factor. The theorem applies to all dimensions and signatures.     

50°视场角投影式头盔光学系统设计及逆反射屏研究

设计了一款适于医疗培训用投影式头盔物镜系统，出瞳直径8mm，视场50°，能够满足对角0．9英寸微显示器对超高分辨SXGA模式的显示要求．其结构紧凑，口径10mm，长度12mm，重量仅有5g．本物镜系统场曲仅0．35D，畸变仅0．64％．为考察本投影式头盔系统的成像特性，研究了不同“逆反射材料”的特性．实验得到高强级逆反射材料在±40°视场范围内反射光强无明显变化，适合做为投影屏幕材料．定量分析了逆反射屏放置位置对成像的影响．     

用射影不变性纠正鱼眼镜头畸变

计算机视觉通常采用针孔摄像机模型，但对于存在较大畸变的鱼眼镜头或广角镜头，必须首先纠正镜头畸变才能应用针孔模型。为了从同时存在透视变形和鱼眼畸变的图像中纠正鱼眼畸变，采用了以下射影不变性：空间中直线的投影为直线；平行直线束的投影平行或相交于一点；直线段投影的交比不变。首先，用待纠正的鱼眼镜头对一幅等间隔正交网格图成像，提取网格结点作为控制点，然后用射影不变性求解畸变模型，达到纠正畸变的目的。该算法巧妙地运用三次方程的Cardan解法。大大提高了速度。结果表明，运用该方法纠正鱼眼镜头畸变速度快、精度高。     

Projective versus metric structures

We present a number of conditions which are necessary for an n-dimensional projective structure (M,[∇]) to include the Levi-Civita connection ∇ of some metric on M. We provide an algorithm, which effectively checks whether a Levi-Civita connection is in the projective class and, which finds this connection and the metric, when it is possible. The article also provides basic information on invariants of projective structures, including the treatment via the Cartan normal projective connection. In particular we show that there are a number of Fefferman-like conformal structures, defined on a subbundle of the Cartan bundle of the projective structure, which encode the projectively invariant information about (M,[∇]).     

A New Scheme to Projective Synchronization of Fractional-Order Chaotic Systems

We demonstrate that the projective synchronization can be observed in coupled fractional-order chaotic systems. A new systematic and powerful coupling scheme is developed to investigate the projective synchronization via the open-plus-closed-loop control, which allows us to arbitrarily manipulate the scaling factor of projective synchronization. The proposed scheme is proved analytically on the basis of the stability theorem of the fractional differential equations. Numerical simulations on the fraction-order chaotic Chen system are presented to justify the theoretical analysis.     

Anti-Selfdual Connections on the Quantum Projective Plane: Monopoles

We present several results on the geometry of the quantum projective plane. They include: explicit generators for the K-theory and the K-homology; a real calculus with a Hodge star operator; anti-selfdual connections on line bundles with explicit computation of the corresponding ‘classical’ characteristic classes (via Fredholm modules); complete diagonalization of gauged Laplacians on these line bundles; ‘quantum’ characteristic classes via equivariant K-theory and q-indices.