Embeddability for Three-Dimensional Cauchy-Riemann Manifolds and CR Yamabe Invariants

Let M^3 be a closed CR 3-manifold. In this paper we derive a Bochner formula for the Kohn Laplacian in which the pseudo-hermitian torsion plays no role. By means of this formula we show that the non-zero eigenvalues of the Kohn Laplacian are bounded below by a positive constant provided the CR Paneitz operator is non-negative and the Webster curvature is positive. Our lower bound for the non-zero eigenvalues is sharp and is attained on S^3. A consequence of our lower bound is that all compact CR 3-manifolds with non-negative CR Paneitz operator and positive CR Yamabe constant are embeddable. Non-negativity of the CR Paneitz operator and positivity of the CR Yamabe constant are both CR invariant conditions and do not depend on conformal changes of the contact form. In addition we show that under the sufficient conditions above for embeddability, the embedding is stable in the sense of Burns and Epstein. We also show that for the Rossi example for non-embedability, the CR Paneitz operator is negative. For CR structures close to the standard structure on $S^3$ we show the CR Paneitz operator is positive on the space of pluriharmonic functions with respect to the standard CR structure on $S^3$.Comment: The new version also proves a partial converse. That is for CR structures close to the standard CR structure on the 3-sphere, embedabillity is shown to imply the non-negativity of the CR Paneitz operator on pluriharmonic functions for the standard CR structure. Typos are corrected, and statement of prop. 1.11 revise

Umbilic hypersurfaces of constant sigma-k curvature in the Heisenberg group

We study immersed, connected, umbilic hypersurfaces in the Heisenberg group $H_{n}$ with $n$ $\geq$ $2.$ We show that such a hypersurface, if closed, must be rotationally invariant up to a Heisenberg translation. Moreover, we prove that, among others, Pansu spheres are the only such spheres with positive constant sigma-k curvature up to Heisenberg translations.Comment: 28 pages, 6 figure

Umbilicity and characterization of Pansu spheres in the Heisenberg group

For $n\geq 2$ we define a notion of umbilicity for hypersurfaces in the Heisenberg group $H_{n}$. We classify umbilic hypersurfaces in some cases, and prove that Pansu spheres are the only umbilic spheres with positive constant $p$(or horizontal)-mean curvature in $H_{n}$ up to Heisenberg translations.Comment: 32 pages, 2 figures; in Crelle's journal, 201

Data Communication Between an Expert System Shell and a Conventional Algorithmic Program With Application to Cam Motion Specification

Although more and more expert system shells have begun to provide communication interfaces to conventional procedural languages, the interfaces are basically shell- and language-dependent. This paper presents a simple, shell- and language-independent data communication technique between a shell and a procedural language via a concept analogous to the handshake data transmission used in microprocessors. A control file is used for the action of handshake. The communication interface is between two data files in two different language environments. A program written in a LISP-based expert system shell, OPS 5, and one written in a procedural language, FORTRAN, were tested to verify the presented technique. An expert system for cam motion specification, which needs the following three tasks—symbolic representation, numerical computation, and their communication—is described as one of the possible applications of the technique. These three tasks are essential to automated engineering design and analysis

Data Communication Between an Expert System Shell and a Conventional Algorithmic Program With Application to Cam Motion Specification

Although more and more expert system shells have begun to provide communication interfaces to conventional procedural languages, the interfaces are basically shell- and language-dependent. This paper presents a simple, shell- and language-independent data communication technique between a shell and a procedural language via a concept analogous to the handshake data transmission used in microprocessors. A control file is used for the action of handshake. The communication interface is between two data files in two different language environments. A program written in a LISP-based expert system shell, OPS 5, and one written in a procedural language, FORTRAN, were tested to verify the presented technique. An expert system for cam motion specification, which needs the following three tasks—symbolic representation, numerical computation, and their communication—is described as one of the possible applications of the technique. These three tasks are essential to automated engineering design and analysis

An Efficient Technique for Finding the Desired Global Optimum of Robotic Joint Displacement

For an industrial robot on a daily operation basis such as pick and place, it is desired to minimize the robotic joint displacements when moving the robot from one location to another. The objective of the optimization here is to simultaneously minimize a robot end effector\u27s positional error and the robotic joint displacements. By modifying the searching algorithm in the existing complex optimization method, this article presents a technique for finding the desired global optimum solution more efficiently. To compare the optimum searching capability between the proposed and existing searching algorithms, a modified Himmelblau\u27s function is used as an objective function. The presented technique is then applied to a spatial three-link robot manipulator for global minimization of the joint displacements

Smart Arduino Sensor Integrated Drone for Weather Indices: Prototype

Mostly, the conditions within an ecosystem as well as weather of a field affect crop productivity greatly. Different weather conditions produce different effects and different impact on the quality of the crop field or the ecosystem. Weather elements form a chain reaction, as the atmosphere is not the only one being affected. Atmospheric air temperature, vapor pressure and relative humidity or moisture content can act together and form diverse effects on crops. These diverse effects turn to reduce radiation which is necessary for plants, or increase rainfall patterns. Consistent high temperatures can increase the heat transfer to local bodies of water in addition to heating the air. Monitoring the climate and the weather conditions are important not only as an environmental baseline, but to maintain quality working conditions, marine studies and recreational safety. The parameters of climate are measurable, for example, atmospheric vapor pressure, temperature, precipitation and solar radiation, can be captured and recorded daily on the Smart Arduino Sensor Integrated Drone. Means and extreme datasets, maximum and minimum weather trends with deviations of lengthy time series would be calculated for each of these climate parameters which were considered in this study. These results are a simple form of climate indices, as they already describe changes in climate. All the readings and datasets are recorded on a cloud platform, as well as, in an installed microchip on the drone. Data synchronization is done with MAT-LAB and Arduino Programming Rule

Growth and characterization of BaZnGa

We report the growth, structure and characterization of BaZnGa, identifying it as the sole known ternary compound in the Ba-Zn-Ga system. Single crystals of BaZnGa can be grown out of excess Ba-Zn and adopt a tI36 structure type. There are three unique Ba sites and three M\,=\,Zn/Ga sites. Using DFT calculations we can argue that whereas one of these three M sites is probably solely occupied by Ga, the other two M sites, most likely, have mixed Zn/Ga occupancy. Temperature dependent resistivity and magnetization measurements suggest that BaZnGa is a poor metal with no electronic or magnetic phase transitions between 2\,K and 300\,K