Resonant Collisions Among Two-Dimensional Localized Waves in the Mel'nikov Equation

We study the resonant collisions among different types of localized solitary waves in the Mel'nikov equation, which are described by exact solutions constructed using Hirota's direct method. The elastic collisions among different solitary waves can be transformed into resonant collisions when the phase shifts of these solitary waves tend to infinity . First, we study the resonant collision among a breather and a dark line soliton. We obtain two collision scenarios: (i) the breather is semi-localized in space and is not localized in time when it obliquely intersects with the dark line soliton, and (ii) the breather is semi-localized in time and is not localized in space when it parallelly intersects with the dark line soliton. The resonant collision of a lump and a dark line soliton, as the limit case of resonant collision of a breather and a dark line soliton, shows the fusing process of the lump into the dark line soliton. Then we investigate the resonant collision among a breather and two dark line solitons. In this evolution process we also obtain two dynamical behaviors: (iii) when the breather and the two dark line solitons obliquely intersect each other we get that the breather is completely localized in space and is not localized in time, and (iv) when the breather and the two dark line solitons are parallel to each other, we get that the breather is completely localized in time and is not localized in space. The resonant collision of a lump and two dark line solitons is obtained as the limit case of the resonant collision among a breather and two dark line solitons. In this special case the lump first detaches from a dark line soliton and then disappears into the other dark line soliton. Eventually, we also investigate the intriguing phenomenon that when a resonant collision among a breather and four dark line solitons occurs, we get the interesting situation that two of the four dark line solitons are degenerate and the corresponding solution displays the same shape as that of the resonant collision among a breather and two dark line solitons, except for the phase shifts of the solitons, which are not only dependent of the parameters controlling the waveforms of the solitons and the breather, but also dependent of some parameters irrelevant to the waveforms.

High Resolution STEM Images of the Human Tooth Enamel Crystals

High-resolution scanning transmission electron microscopy (STEM) images of human tooth enamel crystals, mainly in the high-angle annular dark-field (STEM-HAADF) mode, are presented in this work along the [1000], [10-11]. and [1-210] directions. These images allow knowing some structural details at the nanometric level of the human tooth enamel crystals and of the central dark line (CDL) observed at their centers. The transmission electron microscopy (TEM) and high-resolution TEM (HRTEM) images of the CDL showed the Fresnel contrast. In the STEM bright-field (STEM-BF) and annular-dark-field (STEM-ADF) images, the CDL was observed as an unstrain hydroxyapatite (HAP)-like zone but surrounded by a strained zone. In the STEM-HAADF images, the CDL appeared with a weak contrast, and its contrasts’ thickness was registered between 3 and 8 Å. The arrangement obtained in the STEM-HAADF images by identifying the bright points with the Ca atoms produced the superposition of the HAP atomic sites, mainly along the [0001] direction. The findings provide further information on the structure details at the center of enamel crystals, which favors the anisotropic carious dissolution at the CDL.

Simple and Efficient Realization of Transverse Linear Dark Beams by Azimuthal Phase-Shifted Square Zone Plate

Herein, we are about to introduce a novel, reliable and straightforward method to create controllable dark lines employing an azimuthal square zone plate. As a matter of fact, this diffractive element is a square zone plate whose zones are phase-shifted azimuthally. As we illustrate, one way to construct it is combining a square zone plate and radial grating having period m. Considering its focusing behavior, we came to the result that a dark line surrounded by linear bright zones is generated for odd m, as well as a cross-like dark zone is produced when m is even. Furthermore, we illustrate that the length of the dark lines depends on the grating period. Finally, the simulation predictions are verified by experimental results.

Saint Nicholai Velimirovich: Understanding of War and Peace

The author addresses two important issues in this paper. First, what is a man, and what makes a man great and globally-historically important? In the light of this issue, he writes about Saint Nicholai. The author asserts that the attributes of a great man are intellectual depth, the width of knowledge, the ability to reach God and ontological depths of the world, vails of time and historical human destiny through his action, creation, and writing. All men who are great deal with the issue of man, meaning of life, and inevitability of death. Great men dreamt of immortality in their own glorious ways. What is left behind these giants are permanent unsurpassed deeds and the power of ideas accepted in all ages. The author aims to highlight what makes a man great for his people and for humanity in total, and to what extent does St. Nicholai meet these strict and demanding conditions and criteria to be viewed as a great man; is he great for his people or even outside of these limits. In the second, main issue and part of the paper, the author examines the understanding of war and peace in Bishop Nicholai’s work War and the Bible. The focal point of the examination is the phenomenon of war and peace, and especially the perception of the Bishop’s biblical study of war and peace which differentiates his approach from many other approaches to the phenomenon of war. The theological perspective of the phenomenon of war and peace always implies that good and evil clash in war and peace, and that this conflict is planetary and omnipresent; some individuals are on the side of justness, providence, light, and sanctity of life, while others side with the dark line of life which signifies the rule of evil in our world. According to the author, war is God’s will, just as peace among men. Conflict and peace between nations, as well as spiritual harmony and dissonance in human souls, depend primarily on faith in the Lord. If one is in God’s grace victory is secure. We ought to be reminded of the Christian understanding that the support of all people to one man is futile if he stands against God — on the other hand, he fears nothing if the will of God is on his side, even if all people are against him. In his book, War and the Bible, Bishop Nicholai claims that even in modern times the Lord of Armies decides the victor of every war, just as it was in ancient times. He claims that in modern war, just like in old times, the sinfulness of nations and national leaders and deviation from God’s Laws inevitably brings defeat; in today’s wars, just like in ancient conflicts, justfulness of nations and their leaders brings victory. Bishop Nicholai’s key conclusion is that all wars, both ancient and modern, can only be understood and explained in a biblical light. He devoted his entire very valuable and useful work to this idea, over a hundred years ago.

Two-dimensional new coherent structures of lump-soliton solutions for the Mel’nikov equation

Under investigation in this paper are new novel coherent structures of two-dimensional lump-soliton for the Mel’nikov equation. The Hirota bilinear method and Kadomtsev–Petviashvili hierarchy reduction method are applied to construct a particular family of determinant semi-rational solutions exhibiting various coherent waves to the Mel’nikov equation. We first investigate some novel coherent waves, [Formula: see text]th-order lumps first appear from the [Formula: see text] dark line solitons and finally disappear into those [Formula: see text] dark line solitons after living on the constant background for a very short period. In contrast to the usual lump, those lumps in the coherent structures of lump-soliton are not only localized in two-dimensional space and but also localized in time.

Imaging of Vulva Syringoma With Reflectance Confocal Microscopy

Objectives: To investigate the application of reflectance confocal microscopy (RCM) imaging in diagnosis of vulva syringoma.Methods: Patients with lesions suspicious of syringoma on vulva were enrolled in the study. After informed consent was taken, the lesions were photographed and imaged with RCM. The features of the lesion in confocal images were then analyzed and compared with the biopsy findings for histology correlation.Results: Eleven cases in total were included in the study. The typical RCM features observed in syringoma are the presence of round to oval high refractive, and relatively monomorphous mass of varying sizes in the superficial and middle dermis, usually surrounded with 1–2 layers of light-dark line structures, which were further confirmed by histological evaluation. Ten cases showed classic features of syringoma and 1 case exhibited milia in RCM images.Conclusions: Syringoma has distinct features in RCM imaging, which correlates well with histological findings, highlighting the potential role of RCM in the diagnosis and differential diagnosis of vulva syringoma.

A new species of Moenkhausia (Characiformes: Characidae) from the rio Madeira basin, Brazil, with comments on the evolution and development of the trunk lateral line system in characids

A new species of Moenkhausia is described from the rio Machado drainage, Amazon basin, Brazil. It is diagnosed from congeners by its color pattern, consisting of the concentration of chromatophores on the anterior portion of body scales, the horizontally elongate blotch on caudal peduncle, a bright golden coloration of the dorsal portion of eye when alive, and a dark line crossing the eye horizontally. The new species has variable morphology regarding trunk lateral-line canals. Most fully grown individuals do not have enclosed bony tube in many lateral line scales, resembling early developmental stages of tube formation of other species. This paedomorphic condition is interpreted as a result of developmental truncation. Such evolutionary process may have been responsible for the presence of distinct levels of trunk lateral line reductions in small characids. Variation in this feature is common, even between the sides of the same individual. We reassert that the degree of trunk lateral-line tube development must be used with care in taxonomic and phylogenetic studies, because reductions in the laterosensory system may constitute parallel loss in the Characidae. We suggest the new species to be categorized Near Threatened due to the restricted geographical distribution and continuing decline in habitat quality.

Large enhancement of simultaneous color contrast by white flanking contours

Simultaneous color contrast and assimilation are mutually opposing effects on color appearance, and their magnitude depends on spatial context. The Monnier–Shevell illusion induces a large color shift by a synergy of simultaneous assimilation and contrast using the alternating color of proximal and distant surrounds. The illusion induces a prominent effect along the blue-yellow color axis, but a subtle effect along the orthogonal color axis. In this study, we report an illusion generated by an extremely thin gray line on a cyan background that appears reddish when the line is flanked by thin white contours. We quantified the color appearance of the gray line in a color matching experiment and found that the color shift of the gray line with white contours induced large color shifts. It is also known that luminance contrast between a center and its surrounds affects the magnitude of simultaneous color contrast. However, our color contrast effects were larger for a dark line rather than for a pale line. In contrast, the perceived color shift of the line without the contours increased as the luminance of the gray line increased, supporting the known effect of Kirschmann’s third law. These results indicate that Kirschmann’s third law fails to explain the perceived color shift of our illusion, even after accounting for optical factors like aberrations. Observed color shifts could be explained by an augmented synergy theory based on intensity space, rather than chromaticity.