Existence of parabolic minimizers to the total variation flow on metric measure spaces

We give an existence proof for variational solutions u associated to the total variation flow. Here, the functions being considered are defined on a metric measure space $$({\mathcal {X}}, d, \mu )$$ ( X , d , μ ) satisfying a doubling condition and supporting a Poincaré inequality. For such parabolic minimizers that coincide with a time-independent Cauchy–Dirichlet datum $$u_0$$ u 0 on the parabolic boundary of a space-time-cylinder $$\Omega \times (0, T)$$ Ω × ( 0 , T ) with $$\Omega \subset {\mathcal {X}}$$ Ω ⊂ X an open set and $$T > 0$$ T > 0 , we prove existence in the weak parabolic function space $$L^1_w(0, T; \mathrm {BV}(\Omega ))$$ L w 1 ( 0 , T ; BV ( Ω ) ) . In this paper, we generalize results from a previous work by Bögelein, Duzaar and Marcellini by introducing a more abstract notion for $$\mathrm {BV}$$ BV -valued parabolic function spaces. We argue completely on a variational level.

A pressure indicator for the impact of Iberian wild goat on moss and soils in a Mediterranean climate

In the Sierra de Guadarrama National Park (central Spain), the population of Iberian wild goat, also known as Spanish ibex (Capra pyrenaica) has grown strongly since its reintroduction three decades ago. The plant community is now under heavy browsing pressure due to this high population. A study of the presence of moss on rocks was used herein as the basis for the design of an indicator, named impact on mosses (im), to describe the environmental pressure exerted by the Iberian wild goat in terms of moss removal. Granite and gneiss zones at medium altitudes with continental Mediterranean climate are the most suitable areas for successful application of the indicator. The hypotheses to test are: (1) the indicator will discriminate between areas with different wild goat pressure levels, (2) wild goat pressure will explain a high proportion of moss loss variance, and (3) the im indicator will be useful to establish a mathematical model between wild goat pressure and moss loss. The proposed indicator was analyzed using both statistical and data science techniques. The results support the mentioned hypotheses. Specifically, statistically significant differences were found regarding the impact on mosses between areas with different levels of Iberian wild goat pressure. Thus, a high proportion of the variance was associated with wild goat pressure (80% for high-pressure areas, 56% for low-pressure areas). A modified parabolic function was fit to express the relationship between Iberian wild goat pressure and impact on mosses. In conclusion, the im indicator was shown to be a useful tool to assess pressure due to Iberian wild goat. Therefore, im can help assess and manage Iberian wild goat populations and determine their sustainable levels.

I-V Curves of an Apigenin Dye and Their Analysis by a New Parabolic Function

A new parabolic function for I-V curves’ analysis has been proposed. The new “analytical tool” provides a simple way to describe photophysical processes at an approximately monolayer surface of a dye-sensitized solar cell. It may now be possible to estimate factors such as hole–electron recombination, surface defects, and electron diffusion at the semiconductor layer. The theoretical approach that was previously reported by our group for predicting the photovoltaic performance of potential dye sensitizers has also been validated. The experimental photovoltaic and DFT/TD-DFT data of apigenin and those of the highly rated black dyes were used for the validation.

Justification of the parameters of the floating crop lifter when mowing crops

When harvesting dead plants the reapers and mowers are equipped with crop lifters, which lift and feed dead plants (stems) to the cutter. High-quality work of well-known crop lifters is not always ensured due to poor following the relief of the mowed area. Therefore, the aim of the study was to improve the design of a stem lifter of a mower or header and to justify its parameters experimentally. The floating crop lifter is proposed for the use. It consists of a runner pivotally attached to the base, and the base is attached to the finger bar of the header cutter. A lifting pen is rigidly fixed to the runner at an angle of 35°. Between the base of the runner and the lifting pen, a gas strut with excess pressure is installed. The manufactured laboratory unit made it possible to carry out experimental studies. Implementation of the experimental design and computer processing of the obtained results made it possible to justify the optimal values of a number of indicators of the design of the crop lifter. The smallest material losses (less than 1%) were observed at coded values of the factors: X1 = 0...0.5; X2 = -0.25...0.25; X3 = -0.5...0. This corresponded to the natural values of the studied factors: runner length l = 450-500 mm; the load of the gas strut P = 45-55 N; operating speed of the unit υ = 1.2-1.6 m/s. The obtained exponential dependence on the parabolic function of these factors adequately describes the experimental results.

Pin-ended column buckling load is 2.73% lower than Euler's

A verification calculation was aimed at further proving that the least critical load gives the Euler buckling load for a pin-ended column to be : Pcr=(PI)2*EI/L2. Selecting a parabolic function for this purpose, that meets the boundary conditions and is almost exactly similar to the symmetrical function sin(x). It was expected to obtain a critical load that is larger than the load given by the sine function. The parabolic function produced LOWER CRITICAL LOAD by about 2.73%.

An editor for the generation and customization of geometry restraints

Chemical restraints for use in macromolecular structure refinement are produced by a variety of methods, including a number of programs that use chemical information to generate the required bond, angle, dihedral, chiral and planar restraints. These programs help to automate the process and therefore minimize the errors that could otherwise occur if it were performed manually. Furthermore, restraint-dictionary generation programs can incorporate chemical and other prior knowledge to provide reasonable choices of types and values. However, the use of restraints to define the geometry of a molecule is an approximation introduced with efficiency in mind. The representation of a bond as a parabolic function is a convenience and does not reflect the true variability in even the simplest of molecules. Another complicating factor is the interplay of the molecule with other parts of the macromolecular model. Finally, difficult situations arise from molecules with rare or unusual moieties that may not have their conformational space fully explored. These factors give rise to the need for an interactive editor for WYSIWYG interactions with the restraints and molecule.Restraints Editor, Especially Ligands(REEL) is a graphical user interface for simple and error-free editing along with additional features to provide greater control of the restraint dictionaries in macromolecular refinement.

Morphometric variability of Clitellocephalus ophoni (Eugregarinida, Gregarinidae) in the intestines of Harpalus rufipes (Coleoptera, Carabidae)

Clitellocephalus ophoni (Tuzet and Ormieres, 1956) Clopton, 2002, is one of the parasites of a common ground beetle species, Harpalus rufipes (De Geer, 1774), inhabiting practically the entire temperate zone of Eurasia. Photographs of 177 gamonts and 74 syzygies of C. ophoni from specimens of three populations of H. rufipes collected from the countryside near Dnipropetrovsk (Ukraine), were analyzed according to 15 linear characteristics and 18 indices for gamonts and 6 indices for syzygies. The coefficient of variation (CV) for the majority of linear parameters for gamonts ranged between 28.2-71.3%. Out of 15 linear parameters, only 6 showed a normal distribution; the others showed a statistically significant asymmetry (the maximum indicators on the histogram of distribution were inclined to the area of minimum value). The distribution of all 18 morphological indices diverged from the norm. Two maximum indicators were registered in the disposition of the widest point of the protomerite and deutomerite. The minimum CV was registered for the ratio of gamont length to the length of its deutomerite. The size ratios of the primite and satellite in the syzygies were more constant than the morphological indices for the gamonts. The sex of the host does not affect the length of the protomerite and deutomerite, but does affect their width, the disposition of the nucleus and the widest point of the deutomerite. The length of the protomerite and deutomerite relative to the length of the gamont is better described through linear functions, while their width has a nonlinear dynamic and is better described through parabolic function. The ratio of morphometric indices to total length of C. ophoni gamonts is also better described through nonlinear functions. The data obtained on the morphological variability of C. ophoni needs to be compared with the results for artificially infected individuals of other Harpalus species.

A Precise and Efficient Method to Manipulate the Amplitude of Parabolic Function of Transmission Errors

This paper proposes a system of nonlinear equations to manipulate the amplitude of parabolic function of transmission errors. Firstly, the characteristics of parabolic function of transmission errors are defined. Then, a system of nonlinear equations for manipulating the amplitude of parabolic function of transmission errors is created based on both the conditions of contact and the constraint on the amplitude of function of transmission errors. As the number of independent scalar equations in the system minus the number of unknown parameters is one, one extra design parameter can be applied to manipulate the amplitude of parabolic function of transmission errors. The solution to the extra design variable is automatically, precisely, and efficiently determined by the computer program which is created based on the Newton’s root finding method. The time-consuming manual iterations for trying the value of design variable are eliminated. The proposed method can be applied to both two-and three-dimensional gearing problems. At last, a pair of meshing gears composed of a circular-arc spur gear and an involute spur gear is presented to verify the methodology proposed in this paper.