Critical rationalism faces difficulty in Karl Popper’s Socratic formulation: “I may be wrong, AND you may be right, AND by an effort, we may find the truth.” But the Socratic elenchus, using refutations, can only give us negative knowledge of general principles, which is not the wisdom we seek. Affirmatively, we can only find a collection of opinions to be COHERENT, which is one of many. Francis Bacon proposed an improved elenchus to find general truths. You must take up a limited topic to study, then cross-examine your evidence for AND against its apparent nature. Experiments contrary to evidence AND presumed knowledge are entered as self-contradictions in tables of opposition recorded in an “experimental AND natural history.” Such an account highlights a challenging puzzle if the account is to be made COHERENT. With enough problematized evidence, a COHERENT reading, or a solution of the puzzle, will be unique. Being both COHERENT AND unique, it will be the truth about that limited reality being investigated. Unlike the method of hypothesis (“Anticipating Nature”), deciphering a COHERENT model is “Interpreting Nature,” allowing us to find a general truth on a limited topic. Isaac Newton achieved great success using Robert Boyle’s mechanistic version of this method. Using the “experimental philosophy,” he discovered general principles of optics AND astronomy.

In this paper, a new method based on ray optics AND Kirchhoffs method, using tangential plane approximation for calculating the scattered power from rough surface is proposed. Meanwhile applying the Kernel's approach together with the proposed model, the irregular plane parameters for different irregularities are calculated, AND then the scattered power with respect to different elevation AND azimuthal angles is estimated AND compared with measured data, Kirchhoffs AND stochastic scattering models. It is observed that there is good agreement between results obtained from the proposed model AND measurements. Therefore, it can be concluded that using the proposed model to calculate the path loss in mobile communication leads to a better design AND field estimation than Kirchhoffs or stochastic scattering models. Also in radar cross section estimation, the proposed model can assist us in calculating AND estimating the maximum AND minimum scattered power from rough surface with different degrees of roughness, which is important in radar cross section design AND analysis. In addition, the proposed model in contrast to Kirchhoffs method can be applied to any surface with any distribution function AND different degrees of roughness. Therefore, using the proposed model for calculating scattering power can lead to better results than Kirchhoffs or stochastic scattering models.

Statistical Shape Models are used to interpret shapes. They include mean AND variance of corresponding points of training shapes. One of the most important challenges in building statistical shape models is to establish correct correspondences among lANDmarks in a training set. In this paper, the non-rigid CPD (COHERENT Point Drift) method is used to find correct correspondences among points. This method uses both Deterministic Annealing AND a non-rigid scheme to register two shapes simultaneously. Then, the statistical shape model is built using a rigid transformation. The proposed method is evaluated using Compactness, Generalization ability AND Specificity measures. The built model is compared to models created using the ICP (Iterative Closest Point), TPS-RPM (Thin Plate Spline – Robust Point Matching) AND MDL (Minimum Descreption Length) methods by these metrics. The results show that the proposed method performs like the MDL regarding Specificity measure (0.21±0.06). The Compactness AND Generalization ability measures of the proposed method are very similar to those for the MDL method. The run-time of our proposed method is about 68 seconds which is faster than non-rigid TPS-RPM AND MDL approaches (390 AND 3600 seconds respectively). Our results are superior to the ICP AND TPS-RPM algorithms.

The aim of this paper is to define an abstract quantale framework for extending some properties of the zip rings (studied by Faith, Zelmanowitz, etc.) AND the weak zip rings (defined by Ouyang). By taking as prototype the quantale of ideals of a zip ring (resp. a weak zip ring) we introduce the notion of zipped quantale (resp. weakly zipped quantale). The zipped quantales also generalize the zipped frames, defined by Dube AND Blose in a recent paper. We define the zip (bounded distributive) lattices AND we prove that a COHERENT quantale A is weakly zipped iff the reticulation L(A) of A is a zip lattice. From this result we obtain the following corollary: the COHERENT quantale A is weakly zipped iff the frame R(A) of the radical elements of A is zipped. Such theorems allow us to extend to quantale framework a lot of results obtained by Dube AND Blose for the zipped frames AND for the weak zip rings.

The dynamics of a heterostructure composed of antiferromagnetic AND ferromagnetic layers, separated by a metalic layer, has been investigated. By adjusting the applied magnetic field so that the frequency of one of the antiferromagnetic modes lies in the frequency range of the ferromagnetic layer, COHERENT coupling can be achieved due to interlayer exchange interaction. Moreover, the magnetization dynamics within the magnetic layers induce spin pumping into the metal, generating a spin accumulation in the metallic layer. The spin accumulation generates a spin transfer current from the metal to the magnetic layers, which can result in dissipative coupling between the dynamics of the antiferromagnetic AND ferromagnetic layers. This coupling manifests as level attraction in the system's eigenmodes. The indirect coupling between the dynamics of the magnetic layers can be either COHERENT or dissipative, depending on the thickness of the metallic layer; for thin metallic layers, where interlayer exchange interaction is dominate, COHERENT coupling emerges, whereas in thick layers, where exchange interaction is negligible, dissipative coupling prevails.

For any graph, Weisfeiler AND  Leman assigned the smallest  matrix algebra which  contains the adjacency matrix of the graph. The COHERENT configuration underlying this  algebra for a graph $\Gamma$ is called the COHERENT configuration of $\Gamma$, denoted by $\mathcal{X}(\Gamma)$. In this paper, we study the COHERENT configuration of circular-arc graphs. We give a characterization of the circular-arc graphs $\Gamma$, where $\mathcal{X}(\Gamma)$  is a homogeneous COHERENT configuration. Moreover, all homogeneous COHERENT configurations which are obtained in this way are characterized as a subclass of Schurian COHERENT configurations.

In this paper, we construct the Gazeau-Klauder COHERENT states of a two-dimensional harmonic oscillator on a sphere based on two equivalent approaches. First, we consider the oscillator on the sphere as a deformed (non-degenerate) one-dimensional oscillator. Second, the oscillator on the sphere is considered as the usual (degenerate) two--dimensional oscillator. Then, by investigating the quantum optical properties of the constructed COHERENT states, we study the effect of the space curvature on the properties of the constructed sphere Gazeau-Klauder COHERENT states, according to these two approaches.