On the Unique Solvability of Incomplete Cauchy Type Problems for a Class of Multi-Term Equations with the Riemann–Liouville Derivatives

Incomplete Cauchy-type problems are considered for linear multi-term equations solved with respect to the highest derivative in Banach spaces with fractional Riemann–Liouville derivatives and with linear closed operators at them. Some new existence and uniqueness theorems for solutions are presented explicitly and the analyticity of the solutions of the homogeneous equations are also shown. The asymmetry of the Cauchy-type problem under study is expressed in the presence of a so-called defect, which shows the number of lower-order initial conditions that should not be set when setting the problem. As applications, our abstract results are used in the study of a class of initial-boundary value problems for multi-term equations with Riemann–Liouville derivatives in time and with polynomials of a self-adjoint elliptic differential operator with respect to spatial variables.

REPRESENTATION OF THE PAIRED INTERACTION POTENTIAL IN THE FORM OF MULTIDIMENSIONAL RATIONAL SERIES IN JACOBI VARIABLES FOR MANY-BODY PROBLEMS

Scalar power functions of the form x1 + + xN -v Î are in some cases found in physical problems and applications, especially in many-body problems with paired interactions. There are known decompositions for two vectors in three-dimensional space. In this paper, we consider analogous decompositions with any number of N arbitrary M-dimensional vectors in Euclidean space as a product of a multidimensional rational series with respect to spatial variables and hyperspheric functions on the unit sphere SM-1. Such an advantage of expansion arises in three-body problems when solving the Faddeev equation, where it is known that the main problem is the approximate choice of approximation of interaction potentials, in which the t-matrix scattering elements acquired a separable form.

Investigation of Angular Spectrum of Scattered Inert Gas Ions from the InGaP (001) Surface

It has been shown that this method is quite suitable for surface studies and diagnostics of many component materials. The values of the azimuthal angle of distribution of Ne, Ar and Xe ions scattered from InGaP (001) <110> are obtained. The relationship between the spatial variables of the scattered beam (mainly azimuthal angular spectra) and the type of ions has been established. The correlation between focusing properties of surface semichannel with a type of bombardment ion at the different angle of incidence has been shown.

Do house price-earnings ratios in England and Wales follow a power law? An application of Lavalette’s law to district data

This paper considers Lavalette’s function and its applicability to district house price-earnings ratios. Drawing on work in the urban scaling literature and Zipf’s law, in conjunction with finance theories of pricing and affordability, the paper considers how stable the distribution of ratios is over time, how robust the ranking order of ratios is in the face of variations in affordability over 2004–2019, and proffers an explanation for the shape and movement of the distribution. It draws on issues found in the economic growth literature where sigma-convergence is applied to spatial variables, and a narrowing of the distribution is said to indicate convergence. It proposes that, when plotted over time, the Lavalette exponent and Spearman’s correlation coefficient point to divergence and rank-order stability.

New Irregular Solutions in the Spatially Distributed Fermi–Pasta–Ulam Problem

For the spatially-distributed Fermi–Pasta–Ulam (FPU) equation, irregular solutions are studied that contain components rapidly oscillating in the spatial variable, with different asymptotically large modes. The main result of this paper is the construction of families of special nonlinear systems of the Schrödinger type—quasinormal forms—whose nonlocal dynamics determines the local behavior of solutions to the original problem, as t→∞. On their basis, results are obtained on the asymptotics in the main solution of the FPU equation and on the interaction of waves moving in opposite directions. The problem of “perturbing” the number of N elements of a chain is considered. In this case, instead of the differential operator, with respect to one spatial variable, a special differential operator, with respect to two spatial variables appears. This leads to a complication of the structure of an irregular solution.

The Effects of Lower Extremity Kinesio Taping on Temporal and Spatial Parameters of Gait Initiation in Semi-professional Soccer Players With and Without Functional Ankle Instability

Introduction: The present study aimed to investigate the immediate effects of two types of Kinesio taping on the temporal and spatial variables of gait initiation in individuals with and without Functional Ankle Instability (FAI). Materials and Methods: Thirty semi-professional athletes (15 with and 15 without FAI [control]) were recruited for this study. The gait initiation task was examined before and after the two types of Kinesio taping on a force plate. Temporal (Reaction Phase [RP], Anticipatory Postural Adjustment Phase [APAP]), and spatial variables were recorded and compared between Groups, before and after the tape application. Results: The results of multiple repeated-measure analyses of variance showed no significant differences for “factor” and “Group by factor” interaction effects for any outcome measure (P>0.05). There were no significant differences for Group effects except for the APAP (F=10.27, P=0.003). The APAA was 71.95 ms longer in the FAI Group (476.95±15.87 ms) compared to the control Group (405.04±15.87 ms). Conclusion: Kinesio taping application does not influence any of the gait initiation parameters on the force plate. Participants with FAI demonstrated longer APAP which might be due to recurrent injury and instability during sports or physical activity.

On the nonexistence conditions of solution of two-point in time problem for nonhomogeneous PDE

We investigate the problem with local homogeneous two-point conditions with respect to time for nonhomogeneous PDE of second order in time variable and generally infinite order in spatial variables in the case when the characteristic determinant of the problem identically equals zero. We establish the nonexistence conditions of solution of this problem in the class of entire functions.

Using trait data improves correlation between environment and community data only if abundances are considered

A straightforward way to explore variation between communities is to calculate dissimilarity indices and relate them with environmental and spatial variables. Communities are most often represented by the (relative) abundances of taxa they comprise; however, more recently, the distribution of traits of organisms included in the communities has been shown more strongly related to ecosystem properties. In this study, we test whether taxon- or trait-based dissimilarity is correlated more tightly with environmental difference and geographical distance and how the abundance scale influences this correlation. Our study system is grassland vegetation in Hungary, where we sampled vegetation plots spanning a long productivity gradient from open dry grasslands to marshes in three sites. We considered three traits for vascular plants: canopy height, specific leaf area and seed mass. We obtained field estimates of normalized vegetation difference index (NDVI) as proxy of productivity (water availability) for each plot. We calculated between-community dissimilarities using a taxon-based and a trait-based index, using raw and square-root transformed abundances and presence/absence data. We fitted distance-based redundancy analysis models with NDVI difference and geographical distance on the dissimilarity matrices and evaluated them using variance partitioning. Then, using the pooled data, we calculated non-metric multidimensional scaling ordinations (NMDS) from all types of dissimilarity matrices and made pairwise comparisons using Procrustes analysis. Data analysis was done separately for the three sites.We found that taxonomical dissimilarity matches environmental and spatial variables better when presence/absence data is used instead of abundance. This pattern was mainly determined by the increasing variation explained by space at the presence/absence scale. In contrast to this trend, with trait-based dissimilarity, accounting for abundance increased explained variation significantly due to the higher explanatory power of NDVI. With abundance data, considering traits improved environmental matching to a great extent in comparison with taxonomical information. However, with presence/absence data, traits brought no advantage over taxon-based dissimilarity in any respect. Changing the abundance scale caused larger difference between ordinations in the case of trait-based dissimilarity than with taxonomical dissimilarity.We conclude that considering relevant traits improves environmental matching only if abundances are also accounted for.Supporting informationAdditional graphs supporting the results are presented as appendix.Open researchData used in this research are publicly available from Dryad ###link to be supplied upon acceptance###

Testing a procedure to determine spatial proximity in semi-free-ranging macaque groups

Individuals’ spatial position is affected by social factors. The majority of studies correlating spatial position and social factors have used methods with drawbacks. A more complete method was developed by Dolado & Beltran (2011) in captive animals. The present study aimed to apply a modified version of this method in two semi-free-ranging macaque groups. The proposed method divides group’s surroundings into different subareas, selecting different points in each subarea and calculating the coordinates of these points. We filmed each group and analyzed the videos using an activated time transition recording to determine the individuals’ coordinates. With these data, we calculated spatial variables, allowing us to obtain groups’ spatial patterns. The current method improves on previous procedures and could be applied to larger study areas and groups than the method of Dolado & Beltran (2011), thus representing a viable option for studying spatial distribution patterns in semi-free-ranging macaque groups.