One-dimensional Wiener process with the properties of partial reflection and delay

In this paper, we construct the two-parameter semigroup of operators associated with a certain one-dimensional inhomogeneous diffusion process and study its properties. We are interested in the process on the real line which can be described as follows. At the interior points of the half-lines separated by a point, the position of which depends on the time variable, this process coincides with the Wiener process given there and its behavior on the common boundary of these half-lines is determined by a kind of the conjugation condition of Feller-Wentzell's type. The conjugation condition we consider is local and contains only the first-order derivatives of the unknown function with respect to each of its variables. The study of the problem is done using analytical methods. With such an approach, the problem of existence of the desired semigroup leads to the corresponding conjugation problem for a second order linear parabolic equation to which the above problem is reduced. Its classical solvability is obtained by the boundary integral equations method under the assumption that the initial function is bounded and continuous on the whole real line, the parameters characterizing the Feller-Wentzell conjugation condition are continuous functions of the time variable, and the curve defining the common boundary of the domains is determined by the function which is continuously differentiable and its derivative satisfies the Hölder condition with exponent less than $1/2$.

Cosmological Expansion Rate–Various Measurement Results and Interpretation

Different values of the Hubble constant for extragalactic objects are not considered here. We give a number of examples of the extreme accordance of expansion rates of different fields of knowledge with the cosmological expansion rate. The coincidence of the expansion rates means that a common cause is almost inevitable. All these examples are gravitationally bound in themselves and in this case are subject to cosmological expansion. According to standard theory, this should not happen. We therefore question the common boundary of gravity and expansion for both theoretical and observational reasons and conclude that all gravitationally dominated objects participate in cosmological expansion or scale drift, contrary to general doctrine. The space expands with its contents while numerically maintaining distance, radius, rotation time and density. What is generally interpreted as an expansion is obviously a scale drift with a drift rate that corresponds to the size of the Hubble constant. The Earth is subject to expansion and scale drift. This results in numerically constant measured values. This drift apparently also applies to distant galaxies and other objects. The cosmological red shift is not interpreted here as a Doppler effect and numerical increase in distances, but in accordance with standard theory as an expansion or drift of the space-time scale. The expansion of the radii of galaxies makes the assumption of dark matter superfluous. The continents and our everyday environment are not subject to expansion or scale drift.

The social brain of social media – a physiological boundary to the number of online relations

Based on the research done by Dunbar and the resulting Social Brain Hypothesis, the present study introduced a mathematical model for the development of follower numbers and the number of followed accounts regarding users/influencers of Social Media platforms. Under very simple assumptions the mathematical model suggests that an universal upper bound to follower and followed numbers exists. The theoretical upper bound is then empirically validated by using a representative data set of 255 influencers on Instagram from the field of women’s fashion. The follower numbers show convergence to a common boundary for the years 2018 to 2019 and stagnation for 2019 to 2020, while the number of followed accounts show stagnation for 2018 to 2019 and convergence for 2019 and 2020. The model in conjunction with its empirical validation therefore provides the mathematical background to establish the socio-biological Social Brain Hypothesis in the field of influencer marketing in regards to Social Media platforms.

On the mechanism of formation of the granular structure and interfaces in self-reinforced aluminum nitride

Results of an investigation by scanning electron microscopy methods of the microstructure of self-reinforced aluminum nitride obtained on the basis of aluminum nitride powder and containing 3 mass.% oxygen by plasma-chemical synthesis in the temperature range 1700-2000 °C are presented. Initial aluminum nitride was represented by the wurtzite (2H) phase. Samples were obtained by free sintering in a nitrogen atmosphere. It was established that, during sintering of AlN in the indicated temperature range, three microstructural types of the material and six types of interfaces (three types of intergranular and three types of intragranular ones) formed. The features of the microstructure of the materials are fully determined by the development of intergranular crystal-oriented polytype transitions of 2H AlNmultilayer polytypes (MP) in sintering. The sequence of successive structural transformations that determine the development of polytype transitions was established. 1. Formation of initial 2H AlN grains of the solid solution 2H AlN-O. The substitution of nitrogen by oxygen takes place. 2. The development of isomorphous delamination of the solid solution in every grain with the precipitation of an interlayer enriched in oxygen. 3. In interlayers, polytypes consisting of a series of polytypes with different number of layers (MP) form. Such an interlayer has developed base surfaces and propagates from one boundary to another in the grain, which determines the formation of a special structural state of fragments of boundaries, that border interlayers in the direction <hk0>. 4. The high mobility of the indicated fragments of boundaries determines their break-off from the common boundary and formation of a grain nucleus of anisometric (plate-like) shape. This process begins already at a sintering temperature Tsint. = 1800 °C, and, at Tsint. = 2000 °C, polycrystals practically entirely consist of grains of plate-like shape. In this case, with increase in the sintering temperature, the aspect ratio (the length-to-width ratio) of such grains rises. Keywords: aluminum nitride, polytype transformations, grains, microstructure, boundaries, self-reinforcement.

Measurement of 30-Year Urban Expansion Using Spatial Entropy in Changwon and Gimhae, Korea

Entropy is widely used for measuring the degree of urban sprawl. However, despite the intense use of the entropy concept in urban sprawl, entropy’s spatial context has been largely ignored. In this study, we analyzed urban sprawl in Changwon and Gimhae cities, as they shared a common boundary but differed in their population growth and urban expansion. The land cover type, “urban and dry area,” was used to identify urban areas in the two cities, and a land cover map showed the areas of expansion in the 1980s, 1990s, 2000s, and 2010s. Different zoning schemes, namely concentric rings and regular partitioning, were applied. Shannon’s and Batty’s spatial entropy indices were used to measure urban sprawl. The results showed that concentric ring zoning was not suitable for measuring urban sprawl in a decentralized and polycentric city. Batty’s spatial entropy was less affected by the zoning scheme used and reflected the pattern of urban expansion more accurately. Urban sprawl, a phenomenon occurring within a spatial context, can be better understood by measuring spatial entropy with appropriate zoning schemes.

Textuality standards of goods labels and packaging

This article deals with the food and drink names. Special attention is given to the peculiarities of goods names in the context of textuality. Names of the beverages and eatables verbalize all features, qualities and individual characteristics of these goods. They create the naming space that consists of four nominative components: brand, individual, genitive, and functional descriptive. These nominative components create the text of labels and packages. Four nominative components function as corresponding text information blocks. It means that food and drink names labels combine two spaces. The first space is naming that is represented with the integrated naming complex. The complex grasps four nominative components. The second space is informational that stores the necessary volume of information and creates a communicative background. The information scope is kept in the text construction. The whole volume is divided into four relevant text blocks. Together all these blocks form text boundaries which outline the text construction. This text construction is characterized with two interdependent features coexisting in the integrated naming complex such as cohesion and coherence. Cohesion is realized on the lexical level involving the mechanism of repetition which is the part of the interaction. On the other hand, the repetition may be complete (the naming unit is repeated literally) and partial (the naming unit is repeated partly). The repetition may be between nearest blocks (having common boundary) and distant blocks (without common boundary). There is some peculiarity in the structure of functional-descriptive text block which functions as a set of subblocks. These subblocks are grasped into four subblock clusters. It indicates that description of goods properties and their usage instructions are significant in the text construction of labels and packages. The results of the research broaden the set of naming units adding to word, phrase, and sentence the next unit recognized as a text.

Mass Spring Interlocked Bladed Disk Model

A simplified bladed disk model with cantilever and interlock conditions is described. Blade is composed of three masses, two for the lower and higher part of the shroud, and one for the main core of the blade. A similar scheme is employed in the disk. The different masses in the model are linked with springs introducing the stiffness between them. Additional disk restrictions reduce the model capabilities but account the effect of common boundary conditions. The model simplicity allows an analytical solution with polynomials to understand the fundamentals of vibration. The extended stiffness and mass matrix with Lagrange multipliers are used. The modal frequencies and modes as function of the nodal diameter are studied. The interlock solution is compared to cantilever and different sorts of frequency curves have been identified and classified. Some basic conclusions related to the model parameters are achieved.

Determination of Composite Properties in the Presence of Fiber Deboning and Matrix Damage by Using the Method of Cell

In this study, the elastic properties of composite materials are investigated, considering the effects of separation of fiber-matrix joint boundary and matrix failure. In this method, by assuming periodic microstructure and using a linear approximation of the displacement field by applying continuity and equilibrium conditions, the composite fiber composite relation is determined. The effect of separation is assumed by introducing tangential and normal scalar parameters in the equations by assuming the displacement field jump at the common boundary. In order to express the effect of matrix micro-cracks, the fracture mechanics framework of continuous environments was used and the micro-cracks parallel to the fibers, perpendicular to the fibers and in the thickness direction with scalar parameters were expressed. At the end of the effect of these parameters the results are presented in graphs. The results show that the presence of defective joint at the joint boundary and the matrix micro-components reduce the hardness of the composite and thus it’s bearing load, which is more significant at the defective joint state.

A Resonated and Synchrophased Three Beams Neutron Cancer Therapy Installation

The technique of composite region coupling by a neutron source at a common boundary of different regions that has been introduced in 2019 has allowed for an additive separation of variables neutron-density 3D wave analytical solution to the posing four-regional boundary value problem (BVP) of neutron cancer therapy (NCT). The three employable mutually orthogonal neutron beams, which may have different pulse shapes, have distinct modulation frequencies ω,ϖ, and ŵ and distinct relative time delays ε and ε̂. By employing this solution, we demonstrate in this paper how the therapeutic utility index and the ballistic index for this kind of dynamical NCT form a nonlinear optimization problem. Both of these indices are demonstrated to be remarkably periodically discontinuous in ε or ε̂, even in the neighborhood of the respective ε∗ or ε̂∗. As an extension of a result obtained also in 2019, for a certain lower-dimensional setup, a Pareto optimal control vector ω∗=(ω∗,ϖ∗,ε∗,ŵ∗,ε̂∗) is identified for this 3D problem. The existence of this vector paves the way toward what we call a “resonated and synchrophased three beams neutron cancer therapy (RASP-3BNCT) installation.”

An Improved Hybrid Segmentation Method for Remote Sensing Images

Image segmentation technology, which can be used to completely partition a remote sensing image into non-overlapping regions in the image space, plays an indispensable role in high-resolution remote sensing image classification. Recently, the segmentation methods that combine segmenting with merging have attracted researchers’ attention. However, the existing methods ignore the fact that the same parameters must be applied to every segmented geo-object, and fail to consider the homogeneity between adjacent geo-objects. This paper develops an improved remote sensing image segmentation method to overcome this limitation. The proposed method is a hybrid method (split-and-merge). First, a watershed algorithm based on pre-processing is used to split the image to form initial segments. Second, the fast lambda-schedule algorithm based on a common boundary length penalty is used to merge the initial segments to obtain the final segmentation. For this experiment, we used GF-1 images with three spatial resolutions: 2 m, 8 m and 16 m. Six different test areas were chosen from the GF-1 images to demonstrate the effectiveness of the improved method, and the objective function (F (v, I)), intrasegment variance (v) and Moran’s index were used to evaluate the segmentation accuracy. The validation results indicated that the improved segmentation method produced satisfactory segmentation results for GF-1 images (average F (v, I) = 0.1064, v = 0.0428 and I = 0.17).